Class XII Physics Study Material

KVS ClassXII PHYSICS 1
KENDRIYA VIDYALAYA SANGATHAN
STUDY cum SUPPORT MATERIAL
2014-15
CLASS: XII
PHYSICS( Subject Code:042)
Prepared by: KVS SILCHAR Region

This material was prepared under the patronage of
Sh Avinash Dikshit, IDAS - Commissioner, KVS HQ
Dr Dinesh Kumar - Addl. Commissioner(Acad) , KVS HQ
Dr. (Smt) V. Vijayalakshmi- Joint Commissioner(Acad), KVS HQ
SH. Somit Srivastav Deputy Commissioner KVS (RO) SILCHAR
SH. R. Senthil Kumar ,Assistant Commissioner,KVS (RO) SILCHAR
First Edition : 2011 – 12
Revised Edition: 2013 – 14
Under the Guidance of
Sh.SOMIT SRIVASTAV ,Deputy Commissioner,KVS (RO) SILCHAR
& Sh. R. Senthil Kumar Asst.Commissioner KVS (RO)SILCHAR
Mr. T. P. Gaur , Asstt. Commissioner, KVS ( RO), Silchar
Content Revisedby Mr M.M. KATIYAR Principal, KV Silchar,ASSAM,Pin 788003
&
PGTs (Physics)
1.Mrs. J. A. L.Smith,KV Masimpur 2.Mr. V. N. Jha,KV Silchar

FOREWORD
KVS has been preparing and distributing Study/Support Material in different subjects for
the students of Classes X and XII with the aim of helping them to do well in Board Examinations.
Study/Support Material in Physics for the students of Class – XII in the session 2013-14 which
had significant changes compared to the earlier editions due to the following reasons:
1. Concept Maps indicating inter-relationships between different concepts were included
in each Chapter;
2. Questions were categorized into various special topics in every Chapter;
3. HOTS and probable questions are included in every Chapter.
4. With the Inclusion of one Value Based Question in the Examination Paper ,Now the
Q.P.is reduced Paper to total 29 Question.
While doing so, efforts were made to ensure that it is error free and also the size was
restricted to 167pages, so that it remained as an effective tool for revision at the time of
examination too.
. In this revised edition for the session 2013-14, the following actions have been carried out:
1. The entire text was reviewed and amended to facilitate greater learning;
2. The list of HOTS questions were thoroughly reviewed and repetitions avoided;
3. A separate section listing out the Frequently Asked Questions in the previous Board
Examinations has been included Chapter-wise
4. Inclusion of value based Question Bankof 25 Questions (at the end ) this edition
will help the readers to acquaint themselves with the changed Papern Pattern
5. Two different Model Question papers are included at the end of the material for
the students to prepare/practice for the examination.
We take this opportunity to place on record our appreciation to the all those involved in
updating this edition of the Study/Support Material for their active contributions.
We earnestly hope that this material turns out to be beneficial to all the users.
25.07.2014 SOMITSRIVASTAV
SILCHAR DEPUTY COMMISSIONER
KVS (RO) SILCHAR

1. ELECTROSTATICS
Points to Remember
 Electrostatics is the study of charges at rest.
 Charging a body can be done by friction, induction and conduction.
 Properties of charges:
o An isolated Charge can also exist.
o Like charges repel and unlike charges attract.
o Charges are additive in nature i.e., Q=∑ 𝑞𝑖
𝑛
𝑖=1
o Charges are quantized. i.e., Q= ± ne [n=1,2,3,… & e=1.602 X10-19
C]
o Charge in a body is independent of its velocity.
o Charge is conserved.
 To measure charge electroscopes are used.(Gold leaf electroscope)
 Coulomb’s law: 𝐹⃗ =
𝑘𝑞1 𝑞2
𝑟2
𝑟̂ k=
1
4𝜋𝜀0
= 9X109
Nm2
c-2
Where, 𝜀0= permittivity of free space
Ftotal = F12 + F 13 + ….
 Principle of superposition: 𝐹𝑡𝑜𝑡𝑎𝑙 = ∑ 𝐹𝑖
⃗⃗⃗𝑛
𝑖=1 [vector sum of individual forces]
1 31 2
12 132 2
12 13
1 1 ....
4 4
q qq q
r r
r r  
 
  

Note: In the above triangle the quantity shown at the vertex, could be arrived by multiplying
the quantities shown at the base, ie F=E X Q. Any one of the quantity shown at the base is
givenby the ratio of the quantitiesshownat vertex& the other quantity shown at the base, ie
E=F/Q or Q= F/E
 Electric field: Force experienced by a unit positive (or test) charge. It is a vector. SI unitNC-1
.
 𝐸⃗⃗ =
𝑘𝑄
𝑟2
𝑟̂

0oq
o
F
E Lt
q

ur
ur
It obeys inverse square law
 Field due to a point charge: 𝐸⃗⃗ =
𝑘𝑄
𝑟2
𝑟̂
 Principle of superposition: 1
n
total r
i
E E
 
ur ur
[vector sum of individual fields]
 Dipole: Two equal and opposite charges separated by a small distance.
 Dipole moment:Productof magnitude of charge anddistance of separationbetween them. It is
a vector. SI unit: Cm, 𝑝⃗=Q.2𝑎⃗ ; direction of 𝑝⃗ is negative to positive charge.
F
1/r2 Q1Q2>0
Q1Q2<0
F
QE
1/r2
E
E
r2

 Dipole in a uniform electric field experiences no net force ,instead of force it (electric
Dipole)experiences a torque. 𝜏⃗=𝑝⃗⃗⃗⃗ × 𝐸⃗⃗ ⇒ 𝜏⃗=| 𝑝⃗|| 𝐸⃗⃗|sin 𝜃 𝑛̂
 If 𝜽= 0° ⇒ stable equilibrium; If 𝜽= 𝟏𝟖𝟎° ⇒ unstable equilibrium. (1 Mark)
 Electric field due to a dipole
o at a point on the axial line:
2𝑘𝑝⃗
𝑟3
along the direction of dipole moment
o at a point on the equatorial line:
𝑘𝑝⃗
𝑟3
opposite to the direction of dipole moment.
 Electric flux: ∅=∆𝑆⃗⃗⃗⃗⃗⃗⃗. 𝐸⃗⃗ =| 𝐸⃗⃗||∆𝑆⃗⃗⃗⃗⃗| 𝑐𝑜𝑠 𝜃 ; It is a scalar; SI unit: NC-1
m2
or Vm.
 Gauss’ theorem in electrostatics:∅𝑡𝑜𝑡𝑎𝑙 =
𝑞 𝑡𝑜𝑡𝑎𝑙
𝜀0
 Uniform Charge distribution:
Linear charge distribution: 𝜆 =
∆𝑞
∆𝑙
[𝜆 ⇒linear charge density Unit Cm-1
]
Surface charge distribution: 𝜎 =
∆𝑞
∆𝑆
[𝜎 ⇒surface charge density Unit Cm-2
]
Volume charge distribution: 𝜌 =
∆𝑞
∆𝑉
[𝜌 ⇒ Volume charge density Unit Cm-3
]
 Applications of Gauss’ theorem for uniform charge distribution:
Expression for Infinite
Linear
Infinite plane
sheet
Thin spherical shell
Flux ∅ 𝜆𝑙
𝜀0
𝜎𝑠
𝜀0
𝜎4𝜋𝑟2
𝜀0
Magnitude of
Field E
𝜆
2𝜋𝑟𝜀0
𝜎
𝜀0
𝑄
4𝜋𝑟2 𝜀0
[for points on/outside the shell]
=0 [for points inside the shell]
Charge density
𝜆 =
∆𝑞
∆𝑙
𝜎 =
∆𝑞
∆𝑆
𝜎
4𝜋𝑟2
 Properties of electric field lines:
 Arbitrarily starts from +ve charge and end at –ve charge
 Continuous, but never form closed loops
 Never intersect
 Relative closeness of the field lines represents the magnitude of the field strength.
 For a set of two like charges – lateral pressure in between
 For a set of two unlike charges – longitudinal contraction in between.
 ElectrostaticPotential:Workdone perunitpositive Testcharge tomove itfrominfinitytothat
point in an electric field. It is a scalar. SI unit: J/C or V
V = W / qo
Electric potential for a point charge: 𝑉 =
𝑘𝑞
𝑟

 Electric field is conservative. This means that the work done in moving the charge is
independent of the path followed and the total work done in a closed path is zero.
 Potential due to a system of charges: 1
i
i
i
n kq
rtotal
v 
 Potential due to a dipole at a point
 on its axial line: 𝑉𝑎𝑥𝑖𝑎𝑙 =
𝑘 | 𝑝⃗|
𝑟2
[or]
𝑘| 𝑝⃗|
𝑟2
𝑐𝑜𝑠𝜃
 on its equatorial line:𝑉𝑒𝑞 = 0 (By Puting 𝜃 = 90 )
 Potential difference 𝑉𝐴 − 𝑉𝐵 = 𝑘𝑞 [
1
𝑟 𝐴
−
1
𝑟 𝐵
] ------------𝑟𝐴--------A…………….B
 Potential energy of two charges: U =
𝑘𝑞1 𝑞2
𝑟
 Potential energy of a dipole : U = 𝑝⃗⃗⃗⃗. 𝐸⃗⃗ = p E [𝑐𝑜𝑠𝜃0 - 𝑐𝑜𝑠𝜃1 ]
 Electrostatics of conductors
(i) Inside a conductor Electrostatic field is zero
(ii) On the surface E is always Normal
(iii) No charge inside the conductor but gets distributed on the surface
(iv) Charge distribution on the surface is uniform if the surface is smooth
(v) Charge distribution is inversely proportional to ‘r’ if the surface is uneven
(vi) Potential is constant inside and on the surface
 Equipotential surfaces: The surfaces on which the potential is same everywhere.
 Work done in moving a charge over an equipotential surface is zero.
 No two equipotential surfaces intersect.
 Electric field lines are always perpendicular to the equipotential surfaces.
As E= -
𝑑𝑉
𝑑𝑟
If Vis constant, E ∝
1
𝑟
and if E is constant, V∝ 𝑟
 Capacitor: A device to store charges and electrostatic potential energy.
 Capacitance:
Q
C
V
 , Ratio of charge and potential difference. Scalar,
 SI unit: farad [F]
Capacitance of a parallel plate capacitor: 𝐶 =
𝜀0 × 𝐴
𝑑
q
𝑟𝐵
d

Capacitance of a parallel plate capacitor with a dielectric medium in between:
 Cm =
𝜖 𝑜 𝐴
( 𝑑−𝑡+
𝑡
𝑘
)
 If t=0 =>C0 =
𝜖 𝑜 𝐴
( 𝑑)
 If t=d =>C0 =k
𝜖 𝑜 𝐴
( 𝑑)
=>Cm = k C0
 Combination of capacitors:
Capacitors in series:
1
1 1n
i ic c

Capacitors in parallel :
1
n
i
i
c c


 Energy stored in capacitors:
2
1 1 12
2 2 2
Q
U CV QV
C
  
 Area shaded in the graph = U =
1
2
𝑄𝑉
 Energy density :𝑈𝑑 =
1
2
𝜀0 𝐸2=
𝜎2
2𝜀0
 Introducing dielectric slab between the plates of the charged capacitor with:
Property⇣ Battery connected Battery disconnected
Charge K Q0 Q0
Potential
difference
V0 V0/K
Electric
field
E0 E0/K
Capacitance KC0 KC0
Energy K times
1
2
𝜀0 𝐸2[Energy is supplied
By battery]
1/K times
1
2
𝜀0 𝐸2[Energy used for
Polarization]
 On connecting two charged capacitors:
Common Potential: 𝑉 =
𝐶1 𝑉1+𝐶2 𝑉2
𝑉1+𝑉2
Loss of energy: ∆𝑈 =
1
2
𝐶1 ×𝐶2
𝐶1+𝐶2
( 𝑉1 − 𝑉2)2
 Van de Graff generator:-
V
Q
Cm
Co k

 is an electrostatic machine to build very high voltages.
 works on the Principle 𝑉( 𝑟) − 𝑉( 𝑅) = 𝑘𝑞 (
1
𝑟
−
1
𝑅
) ;
 Coronadischarge is the electrical dischargethroughthe defectedpartof the spherical
conductor,where the surface isnot smooth. Hence,the hollow spherical conductorinthe
Vande Graff generatorshouldhave asmoothoutersurface.
CONCEPT MAP
𝐹 = 𝑘
𝑞1 𝑞2
𝑟2 𝐸 = 𝑘
𝑞1
𝑟2
𝑈 = 𝑘
𝑞1 𝑞2
𝑟
𝑉 = 𝑘
𝑞1
𝑟
Electric Force/Field/Potential/P.E.
(Unit: N) (Unit N/CorV/m)
Electric Force/Field/Potential/P.E.

CONCEPT MAP
Charge and it’s impact

CHARGES AND COULOMB’S LAW
QNo QUESTIONS Marks
1. What isthe workdone inmovinga testcharge ‘q’througha distance of 1 cm alongthe
equatorial axis of anelectricdipole?[ Hint: on equatorial line V=0] 1
2. Why inMillikan’sOil Drop experiment,the charge measuredwasalwaysfoundtobe of some
discrete value and not any arbitrary value?
1
Ans: Because charge is always quantized ie., Q = n x e
3. What is meant by electrostatic shielding? Ans: Electric filed inside a cavity is zero.
1
4. Why an electric dipole placed in a uniform electric field does not undergoes acceleration? 1
Ans: Because the net force on the dipole is zero. Fnet = 0 as F=±𝑞𝐸
5. Why electric field lines
(i) Can never intersect one another?
(ii) Cannot for closed loops sometimes?
(iii) Cannot have break in between?
1
Ans : Because
(i) Electric field has an unique direction at any given point
(ii) Monopoles or single isolated charges exist unlike magnetism
(iii) Start from +ve charges and terminate at –ve charges
6. Showthat at a pointwhere the electricfield intensity is zero, electric potential need not be
zero.
2
Ans: If E = 0⇒ 𝑉 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 E=-dV/dr
7. What is the electric flux through the surface S in Vaccum?
2
8. Write the expression for the electric field, charge density for a uniformly charged thin
spherical shell.
2
Ans: 𝐸 =
𝑘𝑄
𝑟2 ; 𝜎 =
𝑄
4𝜋𝑟2
9.
2
Write the expression for the electric field in the regions I, II, III shown in the above figure.
Ans: EI =EIII = 0 EII = σ/ε0
10. Two free protonsare separatedbya distance of 1 Ao
.if theyare released,whatisthe kinetic
energyof eachproton whenatinfinite separation.[ Hint:at inifinte distance 𝐾. 𝐸 =
𝑒2
4𝜋𝜖 𝑜 𝑟
] 2
11. How does the electric flux, electric field enclosing a given charge vary when the area
enclosed by the charge is doubled? Ans: (a) ∅= constant (b) E is halved
2
12. The electricfieldinacertainregionof space is 𝐸⃗⃗ = 104
𝑖̂𝑁𝐶−1. How muchis the flux passing
throughan area ‘A’if it isa part of XY plane,XZplane,YZ plane,makingan angle 300
with the
axis?
2
+σ
II
-σ
IIII

Ans: ΦXY =10A Vm E ∆S COSφ [φ=0] φXZ= φYZ = 0 Vm (φ =90O
) =104
A cos30O
Vm
13. An electricdipole±4µCis keptat co-ordinate points (1, 0, 4) are kept at (2,-1, 5), the electric
field is given by 𝐸⃗⃗ = 20 𝑖̂ NC-1
. Calculate the torque on the dipole.
2
Ans: Calculate first dipole moment using 𝑝⃗ =q.2𝑎⃗
Then calculate torque using 𝜏⃗ = 𝑝⃗ × 𝐸⃗⃗⃗⃗ and hence find | 𝜏⃗| =13.4 N m
14. Show diagrammatically the configuration of stable and unstable equilibrium of an electric
dipole ( p
ur
) placed in a uniform electric field ( E
ur
).
2
Ans:
Stable Unstable
15. Plot a graph showing the variation of coulomb force F versus
1
𝑟2
where r is the distance
between the two charges of each pair of charges: (1μC, 2μC) and
(2μC, -3μC) Interpret the graphs obtained.
[Hint : graph can be drawn choosing –ve axis for force only]
Ans: | 𝑭 𝑩
⃗⃗⃗⃗⃗⃗| > | 𝑭 𝑨
⃗⃗⃗⃗⃗⃗|
2
16. A thin straight infinitely long conducting wire having charge density 𝜆 is enclosed by a
cylindrical surface of radius r andlengthl,itsaxiscoincidingwiththe lengthof the wire. Find
the expression for electric flux through the surface of the cylinder.
2
Ans: Using Gauss’s Law obtain: Φ =
𝜆𝑙
𝜀0
17. Calculate the force between two alpha particles kept at a distance of 0.02mm in air. 2
Ans: 𝑭 = 𝟗 × 𝟏𝟎 𝟗 𝟒×( 𝟏.𝟔×𝟏𝟎−𝟏𝟗)
𝟐
( 𝟐×𝟏𝟎−𝟓)
𝟐
18. Explain the role of earthing in house hold wiring. 2
Ans: During short circuit, it provides an easy path or emergency way out for the charges
flowing to the ground, preventing the accidents.
19. What is the difference between charging by induction and charging by friction? 2
* In frictional method, transfer of charges takes place from one object to the other.
* During induction, redistribution of charges takes place within the conductor.
20. Two electric charges 3μC, -4μC are placed at the two corners of an isosceles right angled
triangle of side 1 m as shown in the figure. What is the direction and magnitude of electric
field at A due to the two charges?
Ans: E=45×〖10〗^3 NC^(-1)
θ=36.9° from line AB
2
21. A sensitiveinstrumentistobe shiftedfroma strongelectricfieldinitsenvironment. Suggest
a possible way.
[ Hint : Electrostatic shielding ]
2
22. A charge +Q fixedonthe Y axisat a distance of 1m fromthe originand anothercharge +2Q is
fixed on the X axis at a distance of √2 m from the origin. A third charge – Q is placed at the
origin. What is the angle at which it moves?
3
p
ur

E
ur

p
ur

E
ur

A
1 m 3μC4μC
B C
F
1/r2
A
B

ELECTRIC POTENTIAL
Ans:Force due to boththe changesare equal = KQ2
& r
 to each other so the resultant force
will make 45o
with X-axis.
23. Two charges 5µC, -3µC are separated by a distance of 40 cm in air. Find the location of a
point on the line joining the two charges where the electric field is zero.
Ans: Solve for x from the equation: k
5𝑋10−6
𝑥2
= k
3𝑋10−6
(40−𝑥)2
3
24. Deduce Coulomb’s law from Gauss’ law.
Ans:∅=E ⃗.S ⃗=Q/ε0 E×4πr2
=Q/ε0
F=Eq0∴F=〖Qqo/(4πε0 r2
)
3
25. State Gauss’slaw anduse thislaw to derive the electricfiledata pointfroman infinitelylong
straight uniformly charged wire. 3
Ans: Statement . qE ds

  Derivation for E =
2 r


26. Three charges –q, Q and –q are placedat equal distancesona straightline.If the potential
energyof systemof these chargesiszero,thenwhatis the ratioof Q:q [ Ans: 1:4 ] 3
1. Is itpossible thatthe potential atapointis zero,while there isfinite electricfieldintensity
at that point? Give an example.
1
Ans: Yes , Centre of a dipole
2. Is it possible that the electric field 𝐸⃗⃗ at a point is zero, while there is a finite electric
potential at that point. Give an example.
1
Ans: Yes, Inside charged shell
3. Can two equipotential surfaces intersect? Justify your answer. 1
Ans: No. Otherwise it would mean two directions for force at a point.
4. Is potential gradient a vector or a scalar quantity? 1
Ans: Scalar quantity
5. Write the dimensional formula of ‘є0 ‘the permittivity of free space. 1
Ans: [M-1
L-3
T4
A2
]
6. An electricdipoleisplacedinan electric field due to a point charge. Will there be a force
and torque on the dipole?
1
Ans: Yes, Both force and torque will act as the Electric Field is non uniform.
7. Draw the graph showingthe variation of electric potential with distance from the centre
of a uniformly charged shell.
1
Ans
8. Find the ratio of the electric field lines starting from a proton kept first in vacuum and
then in a medium of dielectric constant 6.
1
Ans: 6 : 1
r
V
Distance

9. Calculate the electric field from the equipotential surface shown below. 1
Ans: 2 V [ , 2 , 1 ]
dv
E dv V dr m
dr

  
10. Sketchthe electricfieldlines,whenapositivecharge iskeptinthe vicinityof anuncharged
conducting plate.
1
Ans
11. Two charges are kept as shown. Find dipole moment. 1
Ans: (0,0,2)-q ……………. +q(0,0,-2)
-15 µc +15 µc
12. Compare the electric flux in a cubical surface of side 10 cm and a spherical surface of
radius 10 cm, when a change of 5µC is enclosed by them.
1
Ans: Electric flux will be same in both the cases.
13. Explain why the electric field inside a conductor placed in an external electric field is
always zero.
1
Ans: Charge lies on the surface of a conductor only
14. Two identical metal plates are given positive charges Q1 and Q2,where Q1> Q2. Find the
potential difference between them, if they are now brought together to form a parallel
plate capacitor with capacitance C.
2
Ans: (Q1 – Q2)/2C
15. 27 small drops of mercury having the same radius collage to form one big drop. Find the
ratio of the capacitance of the big drop to small drop.
2
Ans: [3:1]
16. A uniformlychargedrod with linear charge density λ of length L is inserted into a hollow
cubical structure of side ’L’ withconstant velocity and moves out from the opposite face.
Draw the graph between flux and time.
2
4m
3 m
2m
2V 4V 6V
+q
- - - - - -

Ans
17. Draw a graph showingthe variationof potentialwithdistance fromthe positive charge to
negative charge of a dipole, by choosing the mid-point of the dipole as the origin.
2
Ans 2
18. If 𝐸⃗⃗ = 3𝑖̂ +4𝑗̂-5𝑘̂, calculate the electric flux through a surface of area 50 units in z-x plane 2
Ans: 200 unit
19. Name the physical quantities whose SI units are Vm, Vm-1
. Which of these are vectors? 2
Ans: Vm → electric flux, scalar ; Vm-1
→electric field, vector
20. The spherical shell of a Van de Graff generator is to be charged to a potential of 2 million
volt.Calculate the minimumradiusthe shell canhave,if the dielectricstrengthof air is 0.8
kV/mm.
2
Ans: [2.5m]
21. How will you connect seven capacitors of 2µf each to obtain an effective capacitance of
10/11 µf.
2
Ans: 5 in parallel and 2 in series
22. A proton moves with a speed of 7.45 x 105
m/s directly towards a free proton initially at
rest. Find the distance of the closest approach for the two protons.
2
Ans: 5.56 x 10-23
m
23. Three point charges of 1C, 2C & 3C are placed at the corners of an equilateral triangle of
side 1m. Calculate the work done to move these charges to the corners of a smaller
equilateral triangle of sides 0.5m.
2
Ans: 9.9 x 1010
J
24.a Suggestan arrangementof three pointcharges,+q,+q, -qseparatedbyfinite distance that
has zero electric potential energy
2
24. b. Four charges of magnitude Q1,Q2,Q3 ,Q4 have been placed at the corners sharing
one corner eachof a square of side r ,calculate net electrostatic potential energy of the
time
ø
d
O
V
2C
3C

CAPACITORS
S.No
1 What happens to the capacitance of a capacitor when a copper plate of thickness one
third of the separation between the plates is introduced in the capacitor?
2
Ans: 1.5 times Co
2 A parallel plate capacitorischarged and the charging battery is then disconnected. What
happens to the potential difference and the energy of the capacitor, if the plates are
moved further apart using an insulating handle?
2
Ans: Both Increases
3 Find the equivalence capacitance between X and Y. 2
Ans: 9 μf
4 A pithball of mass 0.2 g is hung by insulated thread between the plates of a capacitor of
separation8cm.Findthe potential difference between the plates to cause the thread to
incline at an angle 150
with the vertical, if the charge in the pith ball is equal to 10-7
C.
2
Ans: 429 V
5. Findthe capacitance of arrangementof 4 platesof AreaA at distance d inair as shown. 2
6. What is an equivalent capacitance of the arrangement the shown below 3
system .
25. A pointcharge Q is placedat pointOas shown.Isthe potential difference ( VA-VB) positive,
negative orzeroif Q is (i) positive (ii) negative
2
26. Showthat the potential of a charged spherical conductor, kept at the centre of a charged
hollowspherical conductorisalwaysgreaterthan that of the hollow spherical conductor,
irrespective of the charge accumulated on it.
3
Ans: Va-Vb=(q/4πє) (1/r-1/R)
(Principle of Van de Graff generator)
3 μf3 μf3 μf Y
X

If 6V cell is connected across AD. Calculate the potential difference between B&C.
7. A parallel plate capacitor is charged to a potential difference V by d.c. source and then
disconnected.The distancebetweenthe platesisthenhalved.Explainwithreasonfor the
change in electric field, capacitance and energy of the capacitor.
3
Ans:Use the formulae - Electricfield remainssame,Capacitance doubled, Energy halved
8. Derive anexpressionforcapacitance of parallel plate capacitor, when a dielectric slab of
dielectric constant k is partially introduced between the plates of the capacitor.
3
9. A potential differenceof 1200 V isestablishedbetweentwoparallel plates of a capacitor.
The plates of the capacitor are at a distance of 2 cm apart. An electron is released from
the negative plate, at the same instant, a proton is released from the +ve plate.
(a)How do their (i) velocity (ii) Energy compare, when they strike the opposite plates.
(b) How far from the positive plate will they pass each other?
3
Ans a. (i)42.84 (ii)equal b. 2.7cm
10. Draw a graph to showthe variationof potential applied and charge stored in a capacitor.
Derive the expression for energy stored in a parallel plate capacitor from the capacitor.
3
11. Findthe capacitance of a systemof three parallel plateseachof areaA m2
separatedbyd1
and d2 m respectively. The space between them is filled with dielectrics of relative
dielectric constant є1 and є2.
2
12. Two parallel plate capacitors A and B having capacitance 1µF and 5 µF are charged
separatelytothe same potential 100V. They are then connected such that +ve plate of A
isconnectedto –ve plate of B. Find the charge on each capacitor and total loss of energy
in the capacitors.
3
Ans: 400µC, 500µC and 5/3 x 10J
13. Calculate the capacitance of a systemhavingfive equallyspacedplates,if the areaof each
plate is0.02 m2
and the separationbetweenthe neighboringare 3 mm.in case (a) and (b)
3
Ans: (Hint: Capacitance of a parallel plate capacitor εoA/d )
1.18 x 10-4
μ F and 2.36 x 10 μ F
14. Net capacitance of three identical capacitors in series is 1μf. What will be their net
capacitance if connected in parallel?
Find the ratio of energy stored in the two configurations, if they are both connected to
the same source.
2
Ans: 9μf 1 : 9
15. Two parallel plate capacitors X and Y have the same area of plates and the same
separation between them. X has air between the plates and Y contains a dielectric
medium of εr=4. Calculate Capacitance of X and Y if equivalent capacitance of
V
q

combination is 4 µF.
(i) Potential Difference between the plates of X and Y
(ii) What is the ration of electrostatic energy stored in X and Y
[ Ans : 5 µF, 20 µF, 9.6 V, 2.4 V, 4:1 ]
15. Derive the expressionforenergydensityof aparallel plate capacitor.
16.Prove that netenergystoredacrossthe seriescombinationof three capacitorsremainssame tothat
inparallel combinationof the same three capacitor connectedtothe same source of potential.
2. CURRENT ELECTRICITY
Points To remember
 Currentcarriers – The charge particleswhichflow inadefinitedirection constitutes the electric
current are called current carriers. Example: Electrons in conductors, Ions in electrolytes,
Electrons and holes in semi-conductors.
 Electric current is defined as the amount of charge flowing through any cross section of the
conductor in unit time. I = Q/t.
 Current density J = I/A.
 Ohm’slaw:Currentthrougha conductor isproportional tothe potential difference across the ends of
the conductor providedthe physical conditionssuchastemperature,pressure etc.Remainconstant. V
α I i.e. V = IR, Where R is the resistance of the conductor. Resistance R is the ratio of V & I
 Resistance is the opposition offered by the conductor to the flow of current.
 Resistance R = ρl/A where ρ is the resistivity of the material of the conductor- length and A area of
cross sectionof the conductor.If l is increasedntimes,new resistance becomesn2
R.If A isincreasedn
times, new resistance becomes R
n2
1
 Resistivity ρ = m/ne2
τ,Where m,n,e are mass,numberdensityandcharge of electron respectively, τ-
relaxation time of electrons. ρ is independent of geometric dimensions.
 Relaxation time is the average time interval between two successive collisions
 Conductance of the material G =1/R and conductivity σ=1/ρ
 Drift velocity is the average velocity of all electrons in the conductor under the influence of applied
electric field. Drift velocity Vd = (eE/m)τ also I = neAvd
 Mobility (μ) of a current carrier is the ratio of its drift velocity to the applied field dV
E
 
 Effect of temperature on resistance: Resistance of a conductor increase with the increase of
temperature of conductor (1 )T oR R T  , where α is the temperature coefficient of resistance of
the conductor. α is slightly positive for metal and conductor, negative for semiconductors and
insulators and highly positive for alloys.
 Combination of resistors: 1 2 ...series nR R R R   ,
1 2
1 1 1 1
...
Parallel nR R R R
  
 Cells: E.M.F of a cell is defined as the potential difference between its terminals in an open circuit.
Terminal potential difference of a cell is defined as the p.d between its ends in a closed circuit.
 Internal resistance rof a cell isdefinedasthe oppositionofferedbythe cell tothe flow of current. r =
R
V
E






1 where R is external resistances.
 Grouping of cells :
i) In series grouping circuit current is given by s
nE
I
R nr


,

ii) Inparallel groupingcircuitcurrentisgivenby p
mE
I
r mR


where n,m are numberof cellsin series
and parallel connection respectively.
 Kirchhoff’s Rule:
i) Junction Rule:-The algebraic sum of currents meeting at a point is zero. 0I 
ii) Loop rule:-The algebraic sum of potential difference around a closed loop is zero V o
 Wheatstone bridge isanarrangementof fourresistorsarrangedinfourarms of the bridge and is used
to determine the unknown resistance in terms of other three resistances. For balanced Wheatstone
Bridge,
P R
Q S

 Slide Wire Bridge or Metre Bridge is based on Wheatstone bridge and is used to measure unknown
resistance. If unknown resistance S is in the right gap, R
l
l
s 




 

100
 Potentiometer is considered as an ideal voltmeter of infinite resistance.
 Principle of potentiometer:The potentialdrop across any portion of the uniform wire is proportional
to the length of that portion of the wire provided steady current is maintained in it i.e. v α l
 Potentiometerisused to(i) compare the e.m.f.sof twocells(ii) determine the internal resistance of a
cell and (iii) measure small potential differences.
 Expressionfor comparison of e.m.f of two cells by using potentiometer,
2
1
2
1
l
l



where 21, ll are the
balancing lengths of potentiometer wire for e.m.fs 1 and 2 of two cells.
 Expression for the determination of internal resistance of a cell I is given by R
l
ll





 
2
21
Where 1l isthe balancing length of potentiometer wire corresponding to e.m.f of the cell, 2l that of
terminal potentialdifferenceof the cell whenaresistance Risconnectedinserieswiththe cell whose
internal resistance is to be determined
 Expression for determination of potential difference
L
rl
rR
V 








 . where L is the length of the
potentiometerwire,l isbalancinglength,risthe resistance of potentiometer wire, R is the resistance
included in the primary circuit.
 Joule’s law of heating states that the amount of heat produced in a conductor is proportional to (i)
square of the currentflowingthroughthe conductor,(ii) resistance of the conductor and (iii) time for
which the current is passed. Heat produced is given by the relation H=I2
Rt
 Electric power: It is defined `as the rate at which work is done in maintaining the current in electric
circuit. P =VI = I2
R =V2
/R. Power P is the product of V & I
 Electrical energy: The electrical energy consumed in a circuit is defined as the total work done in
maintainingthe currentinanelectrical circuit for a given time. Electrical energy = VIt = I2
Rt =(V2
/R)t =
Pt
 Commercial unit of energy 1KWh= 3.6×106
J
 Colour coding : Black Brown Red Orange Yellow Green Blue Violet Gray White
0 1 2 3 4 5 6 7 8 9
Tolerance (i) Gold 5% (ii) Silver 10%(iii) No Color 20%
Example: if colour code on carbon resister is Red Yellow and Orange with tolerance colour as silver,
the resistance of the give resister is (24×103
± 10%)Ω

CONCEPT MAP
QUESTIONS
DRIFT VELOCITY, CURRENT, POTENTIAL DIFFERENCE, OHM’S LAW AND RESISTANCE
1. How does the drift velocity of electrons in a metallic conductor vary with increase in temperature?
Ans. remains the same
2. Two different wires X and Y of same diameter but of different materials are joined in series and
connectedacrossa battery.If the numberdensityof electronsinX is twice that of Y, find the ratio of
drift velocity of electrons in the two wires.
Ans: Vdx/Vdy = ny/nx = ½
3.* A 4Ω non insulated wire is bent in the middle by 1800
and both the halves are twisted with each
other. Find its new resistance?
Ans: 1Ω
4. Can the terminal potential difference of a cell exceed its emf? Give reason for your answer.
Ans: Yes, during the charging of cell.
(1)
(1)
(1)
(1)
E
Flow of Charges

5. Two wiresof equal lengthone of copperandthe otherof manganinhave the same resistance.Which
wire is thicker?
Ans: Manganin.
6. The V-I graph for a conductor makes angle Ѳ with V- axis, what is the resistance of the conductor?
Ans: R = Cot Ѳ
7. It is found that 1020
electrons pass from point X towards another point Y in 0.1s. How much is the
current & what is its direction? Ans: 160A; from Y to X
8. Two square metal platesA and B are of the same thicknessandmaterial.The side of Bistwice that of
side o fA. If the resistance of A and B are denoted by RA and RB, find RA/ RB. Ans: 1
9*.The V-Igraph of two resistorsintheirseriescombinationisshown.Whichone of these graphsshows
the series combinations of the other two? Give reason for your answer.
I Ans: 1
V
10. Plot a graph showing the variation of conductivity  with the temperature T in a metallic conductor.
(Ans: see fig1)
R

T D
Fig 1 fig2
11. Draw a graph to showthe variationof resistance Rof the metallicwire asafunctionof itsdiameterD
keeping the other factor constant. (Ans: see fig2)
12. Two conductingwiresXandY of same diameterbutdifferent materials are joined in series across a
battery. If the number density of electrons in X is twice that in Y, find the ratio of drift velocity of
electrons in the two wires. (Ans: I nvd i.e. Vdx/Vdy = ny/nx = ½)
13 A pd of 30V is applied across a colour coded carbon resistor with rings of blue, black and yellow
colours. What is the current to the resistor? Ans: R = 60 × 104
Ω , I= 5× 10-5
A
14. A non-conductingringof radiusrhas charge q distribute overit.Whatwill be the equivalent current
if it rotates with an angular velocity ω? Ans: I= q/t = qω/2π
15.* Two cells each of emf E and internal resistances r1 and r2 are connected in series to an external
resistance R. Can a value of R be selected such that the potential difference of the first cell is 0.
Ans: I = 2Ɛ/(R + r1 + r2) Potential diff. for first cell V1 = Ɛ – I r1 = 0
Ɛ = (2 Ɛ r1)/R + r1 + r2 Solving these we get, R = r1 - r2
16. Why does Resistance increase in series combination and decrease in parallel combination
Ans: Effective length increases in series combination (R α l).
In parallel combination area of cross section increases (R α 1/A)
17. A piece of silver wire has a resistance of 1Ω. What will be the resistance of the constantan wire of
one thirdof itslengthandone half of itsdiameterif the specific resistance of the constantan wire is
30 times than that of the silver? Ans: 40Ω
18. Calculate the current shown by the ammeter in the circuit in fig 1
(1)
(1)
(1)
(1)
(1)
(2)
(2)
(2)
(2)
(2)
(2)
(2)
(2)

10Ω
5Ω
10Ω
10Ω 10Ω
10Ω
+
-
10V
5Ω
A
10Ω 10Ω 10Ω
A
D
B
C
10Ω10Ω10Ω
10Ω10Ω
Fig 1. Fig 2.
Ans: R = 2Ω and I = 5A
19.* The plot in fig 2 given above shows the variation of current I through the cross section of a wire
over a time interval of 10s. Find the amount of charge that flows through the wire over this time
period. Ans: Area under the I-t graph, q = 37.5C
20. Find the resistance between the points (i) A and B and (ii) A and C in the following network
Ans: (i) RAB = 27.5Ω (ii) RAC = 30Ω
21. Two wires of the same material having lengths in the ratio 1:2 and diameter 2:3 are connected in
series with an accumulator. Compute the ratio of p.d across the two wires
Ans: R = ρl/A = 4ρl/πd2
RA/RB = 9/8 VA/VB = IARA/IBRB = 9/8
22. 4 cells of identical emf E1, internal resistance r are connected in series to a variable resistor. The
followinggraphshowsthe variationof terminal voltage of the combinationwiththe current output.
(i)What is the emf of each cell used?
(ii)For what current from the cells, does maximum power dissipation occur in the circuit?
(iii)Calculate the internal resistance of each cell
23.* An infinite ladder network of resistances is constructed with 1Ω and 2Ω resistances shown
5 t(s) 100
I(A)
Ans:4E = 5.6 E = 1.4 V
WhenI = 1A, V = 2.8/4 = 0.7V
Internal resistance, r= (E – V)/I= 0.7Ω
The outputpoweris maximumwheninternal
resistance =external resistance =4r.Imax = 4E/
(4r +4r) = 1A
(2)
(2)
(3)
(3)
(2)

A 6V battery between A and B has negligible resistance.
(i) Find the effective resistance between A and B.
𝑅 =
2𝑅
𝑅+2
+ 1 𝑅 = 2Ω
24. The resistance of a tungsten filament at 150°C is 133Ω. What will be its resistance at 5000
C? The
temperature coefficient of tungsten is 0.00450
C-1
at 00
C.
Ans: Use Rt = R0 (1+ α t) R500 = 258Ω
25. The circuit shown in the diagram contains two identical lamps P and Q. What will happen to the
brightness of the lamps, if the resistance Rh is increased? Give reason.
Ans: Brightness of P and Q decrease and increase respectively.
26. A battery has an emf E and internal resistance r. A variable resistance R is connected across the
terminals of the battery. Find the value of R such that (a) the current in the circuit is maximum (b)
the potential difference across the terminal is maximum. (c)Plot the graph between V and R
Ans: (a) I = Ɛ / (r + R) I = Imax when R =0 Imax = Ɛ /r
(b)V = Ɛ R/(r + R) = Ɛ /(r/R + 1) V = Vmax when r/R + 1= minimum, r/R = o, V= Ɛ
(c)
V
II. KIRCHHOFF’S RULE AND APPLICATIONS
1. Using Kirchhoff’s laws, calculate I1, I2 andI3
Ans: I1 = 48/31A I2 = 18/31A I3 = 66/31A
2. In the circuit, find the current through the 4Ω resistor.
Ans: I = 1A
III. WHEATSTONE BRIDGE AND POTENTIOMETER
1. The emf of a cell used in the main circuit of the potentiometer should be more than the potential
difference to be measured. Why?
2. The resistance in the left gap of a metre bridge is 10Ω and the balance point is 45cm from the left
end. Calculate the value of the unknown resistance. Ans S = 12.5Ω
3. How can we improve the sensitivity of a potentiometer? (1)
4. Why is potentiometer preferred over a voltmeter? (1)
Ans:Since the circuitis infinitelylong,itstotal resistance remainsunaffectedbyremovingone
meshfromit.Let the effective resistanceof the infinite networkbe R,the circuitwill be
(3)
(3)
(3)
(1)
(1)
(3)
R
(3)

5. Write the principle of (2)
(i) a meter bridge.
(ii) a potentiometer.
6. How does the balancing point of a Wheatstone bridge get affected when (2)
i) Position of cell and Galvanometer are interchanged?
ii) Position of the known and unknown resistances is interchanged?
7. Explain with a neat circuit diagram, how will you compare emf of two cells using a potentiometer?
8. With the help of a circuit diagram, describe the method of finding the internal resistance of the
Primary Cell using a potentiometer. (3)
9. With the help of a neat circuit diagram describe the method to determine the potential difference
across the conductorusing a potentiometer. (3)
10. Calculate the current drawn from the battery in the given network.
Ans: I = 2A
11. Find the value of X and current drawn from the battery of emf 6V of negligible internal resistance
Ans: X = 6Ω and I = 1A
12. Findthe value of the unknown resistance X and the current drawn by the circuit from the battery if
no current flows through the galvanometer. Assume the resistance per unit length of the wire is
0.01Ωcm- 1
.
Ans: X = 3Ω
13. In the circuitshown,ABis a resistance wire of uniform cross – section in which a potential gradient
of 0.01V cm-1
exists.
(a)If the galvanometer G shows zero deflection, what is the emf Ɛ1 of the cell used?
(b)If the internal resistance of the drivercell increasesonsome account,how will itaffectthe balance
point in the experiment?
Ans: (a) PD VAB = 1.8 V (b) Balance pt. will shift towards B since V/l decreases.
14.* In a potentiometercircuit,abatteryof negligible internalresistance issetupas showntodevelop a
constantpotential gradientalongthe wire AB.Twocellsof emfs Ɛ 1 and Ɛ2 are connected in series as
shown in the combination (1) and (2). The balance points are obtained respectively at 400cm and
240cm from the point A. Find (i) Ɛ 1/ Ɛ2 and (ii) balancing length for the cell Ɛ 1 only.
battery
Ans : Ɛ1 + Ɛ2 α 400, Ɛ 1- Ɛ2 α 240,Solving Ɛ1/ Ɛ2 = 4, Ɛ1 α l1,
(Ɛ1 + Ɛ2)/ Ɛ1= 400/l1 , l1 = 320cm
(3)
(3)
(3)
(3)
(3)

15.* A potentiometer wire of length 100cm having a resistance of 10Ω is connected in series with a
resistance and cell of emf 2V of negligible internal resistance. A source emf of 10mV is balanced
against a length of 40cm of potentiometer wire. What is the value of the external resistance?
Ans: I = E/(R + 10) = (2/R + 10) Resistance of 40cm
wire is 4Ω. At J, (2/R +10) x 4 = 10 x 10-3
R = 790Ω
16.* In the potentiometer circuit shown, the balance point is at X.
State with reason where the balance point will be shifted
when
(i)Resistance R is increased, keeping all parameters unchanged.
(ii)Resistance S is increased keeping R constant.
(iii)Cell P is replaced by another cell whose emf is lower than that of that cell Q.
Ans: (i) As R is increased V/l will decrease hence X will shift towards B.
(ii)No effect (iii) Balance point is not found.
17.* A potentiometerwire hasalengthL andresistance R0. It is connected to a battery and a resistance
combination as shown. Obtain an expression for the potential difference per unit length of the
potentiometerwire.Whatisthe maximumemf of a ‘testcell’forwhichone can geta balance point
on this potentiometer wire? What precautions should one take while connecting this test cell to
the circuit?
Ans: Total resistance of potentiometer wire R = R0 + RS/(R+S)
Current in the circuit I = E/ (R0 + (RS/R+S))
Total potential difference across AB V = I R0 = E R0/ (R0 + (RS/R+S))
Therefore, PD per unit length is V/L = E R0/L (R0 + (RS/R+S))
Max emf of a test cell should be less than V.
Precaution: Positiveterminal of the testcell mustbe connectedtopositiveterminalof the battery.
18. The variation of potential difference V with length l in case of two potentiometers X and Y as
shown. Which one of these will you prefer for comparing emfs of two cells and why?
Ans: The potentiometer Y is preferred, as it has low potential gradient (V/l)
19. Two cells of emfs Ɛ1 and Ɛ2 (Ɛ1> Ɛ2) are connected as shown in figure
When a potentiometer is connected between A and B, the
balancing length of the potentiometer wire is 300cm. On
E =10mV
(3)
(3)
(3)

connectingthe same potentiometer between A and C, the balancing length is 100cm. Calculate the
ratio of Ɛ1 and Ɛ2.
Ans: Ɛ1 α 300, Ɛ1 – Ɛ 2 α 100, Ɛ1/Ɛ2 = 3/2
IV. ELECTRIC ENERGY AND POWER
1. What is the largest voltage you can safely put across a resistor marked 98Ω - 0.5W?
2. Which lamp has greater resistance (i) 60W and (ii) 100W when connected to the same supply?
Ans: R = V2
/P, R α 1/P, 60 lamp has more resistance
3. Nichrome andCu wires of the same length and same diameter are connected in series in an electric
circuit. In which wire will the heat be produced at a higher rate? Give reason.
Ans: P = I2
R P α R Heat produced is higher in Nichrome wire.
4.* An electric bulb rated for 500W at 100V is used in circuit having a 200V supply. Calculate the
resistance R that must be put in series with the bulb, so that the bulb delivers 500W.
Ans: Resistance of bulb=V2
/P = 20Ω, I = 5A, for the same power dissipation, current should be 5A
when the bulb is connected to a 200V supply. The safe resistance R’ = V’/I = 40Ω. Therefore, 20Ω
resistor should be connected in series.
5. Two bulbs are marked 220V-100W and 220V-50W. They are connected in series to 220V mains. Find
the ratio of heat generated in them.
Ans: H1/H2 = I2
R1 /I2
R2 = R1/ R2= ½
6.* Can a 30W, 6V bulb be connected supply of 120V? If not what will have to be done for it?
Ans: Resistance of bulb R= V2
/P = 36/30 = 1.2Ω Current capacity of the bulb I = P/V = 5A
A resistance R’ to be added in series with the bulb to have current of 5 A, I = V’/R + R’ =5, R’ = 22.8Ω
3.MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
GIST
MAGNETIC EFFECTS OF CURRENT AND MAGNETISM:
1. Magnetic field:
It isa regionarounda magnetor currentcarrying conductorinwhichits magneticinfluence can
be felt by a magnetic needle.
2. Biot-Savart Law
dB =μ0 IdlSinθ/4πr2
μ0=4π x 10-7
Tm/A
[Direction of dB can be found by using Maxwell’s Right hand thumb rule.]
3. Applications :
Magnetic field at a centre of a current carrying circular coil B= μ0I/2a
Magnetic field at a point on the axis of current carrying coil. B= μ0Nia2
/2(a2
+x2
)3/2
(N=no. of
turns in the coil)
4. Ampere’s circuital law
It statesthat the line integral of magneticfieldaroundanyclosedpathin vacuum/air is μ0 times
the total current threading the closed path.
∫ B. dl= μ0 I
5. Applications
i) Magnetic field due to straight infinitely long current carrying straight conductor.
(1)
(1)
(2)
(2)
(3)
(2)

B= μ0 I/2πr
ii) Magnetic field due to a straight solenoid carrying current
B= μ0n I
n= no. of turns per unit length
iii) Magnetic field due to toroidal solenoid carrying current.
B= μ0N I / 2πr
N= Total no. of turns.
6. Force on a moving charge [ Lorentz Force]
(i) In magnetic field F=q(V x B)
(ii) In magnetic and electric field F=q[E+(ν x B)] Lorentz force
7. Cyclotron
(i) Principle
(a) When a charged particle moves at right angle to a uniform magnetic field it describes
circular path.
(b) An ion can acquire sufficiently large energy with a low ac voltage making it to cross the
same electric field repeatedly under a strong magnetic field.
(ii) Cyclotron frequency or magnetic resonance frequency
ν=qB/2πm, T=2πm/Bq; ω=Bq/m
(iii)Maximum velocity and maximum kinetic energy of charged particle.
Vm=Bqrm/m
Em=B2
q2
rm
2
/ 2m
8. Force on a current carrying conductor in uniform
F= (I l x B)
l=length of conductor
Direction of force can be found out using Fleming’s left hand rule.
9. Force per unit length between parallel infinitely long current carrying straight conductors.
F/l= μ0 I1 I2/2πd
(a) If currents are in same direction the wires will attract each other.
(b) If currents are in opposite directions they will repel each other.
10. 1 Ampere – One ampere is that current, which when flowing through each of the two parallel
straight conductors of infinite length and placed in free space at a distance of 1m from each
other, produces between them a force of 2x10-7
N/m of their length.
11. Torque experienced by a current loop in a uniform B.
τ = NIBA Sinθ
τ=MXB
Where M=NIA
12. Motion of a charge in
(a) Perpendicular magnetic field F=q(vxB),F=qvBSin90=qvB (circular path)
(b) Parallel or antiparallel field F=qvBSin0 (or) qvBSin180=0(Straight-line path)
If 0<θ<90 , the path is helix
v Cosθ is responsible for linear motion v, v Sinθ is responsible for circular motion
Hence trajectory is a helical path
13. Moving coil galvanometer
It is a sensitive instrument used for detecting small electric Currents.

Principle: When a current carrying coil is placed in a magnetic field, it experiences a torque.
I αθ andI = K θ where K= NAB/ C
Current sensitivity, Is= θ / I=NBA/K
voltage sensitivity, Vs= θ /V=NBA/KR
Changing N -> Current sensitivity changes but Voltage Sensitivity does not change
(a) Conversion of galvanometer into ammeter
A small resistance S is connected in parallel to the galvanometer coil
S=IgG/( I - Ig) ; RA=GS/(G+S)
(b) Conversion of galvanometer into a voltmeter.
A high resistance R is connected in series with the galvanometer coil.
R=( V/Ig ) –G ; Rv=G+R
Current loop as a magnetic dipole
Magnetic dipole moment M=
2
evr
M=n( eh / 4πme)
14. Representation of uniform magnetic field.
B

15. Magnetic dipole moment of a magnetic dipole.
M=m (2l) SI unit of M -> ampere metre m= pole strength.
The magneticpermeabilityof a material maybe definedasthe rationof magneticinductionB to the
magnetic intensity H
µ=B/H
2
Torque experiencedbya
magneticdiploe inuniform
magneticfield
τ=MXB

magnetic

22. Properties of magnetic substances
DIA PARA FERRO
1. Diamagneticsubstancesare
those substanceswhichare
feeblyrepelledbyamagnet.
Eg. Antimony,Bismuth,Copper,
Gold,Silver,Quartz,Mercury,
Alcohol,water,Hydrogen,Air,
Argon,etc.
Paramagneticsubstancesare
feeblyattractedbya magnet.
Eg. Aluminium,Chromium, Alkali
and Alkalineearthmetals,
Platinum, Oxygen,etc.
Ferromagneticsubstancesare
stronglyattractedby a magnet.
Eg. Iron,Cobalt,Nickel,
Gadolinium, Dysprosium,etc.
2. When placedinmagnetic
field,the linesof force tendto
avoidthe substance.
The linesof force prefertopass
throughthe substance rather
than air.
The linesof force tendto crowd
intothe specimen.
3. When placedinnon-uniform
magneticfield,itmovesfrom
strongerto weakerfield (feeble
repulsion).
Whenplacedinnon-uniform
weakertostrongerfield(feeble
attraction).
Whenplacedinnon-uniform
weakertostrongerfield(strong
attraction).
4. Whena diamagneticrod is
freelysuspendedinauniform
magneticfield,italignsitself ina
directionperpendiculartothe
field.
Whena paramagneticrod is
directionparalleltothe field.
Whena paramagneticrod is
directionparalleltothe field
veryquickly.
5. If diamagneticliquidtakenin
a watch glassis placedin
uniformmagneticfield,it
collectsawayfromthe centre
whenthe magneticpolesare
closerand collectsatthe centre
whenthe magneticpolesare
farther.
If paramagneticliquidtakenina
watch glassisplacedinuniform
magneticfield,itcollectsatthe
centre whenthe magneticpoles
are closerandcollectsaway
fromthe centre whenthe
magneticpolesare farther.
If ferromagneticliquidtakenina
watch glassisplacedinuniform
magneticfield,itcollectsatthe
centre whenthe magneticpoles
are closerandcollectsaway
fromthe centre whenthe
magneticpolesare farther.
6. InducedDipole Moment(M)
isa small – ve value.
InducedDipole Moment(M) isa
small + ve value.
InducedDipole Moment(M) isa
large + ve value.

7. Intensityof Magnetisation(I)
has a small – ve value.
Intensityof Magnetisation(I)
has a small + ve value.
has a large + ve value.
8. Intensityof Magnetisation(I)
has a small + ve value.
has a large + ve value.
9. Magneticpermeability μis
alwayslessthanunity.
Magneticpermeability μismore
than unity.
Magneticpermeability μislarge
i.e.muchmore than unity.
10. Magnetic susceptibilitycm
Magneticsusceptibilitycm hasa
small + ve value.
Magneticsusceptibilitycm hasa
large + ve value.
11. Theydo notobeyCurie’s
Law. i.e.theirpropertiesdonot
change withtemperature.
TheyobeyCurie’sLaw.Theylose
theirmagneticpropertieswith
rise intemperature.
TheyobeyCurie’sLaw.Ata
certaintemperature calledCurie
Point,theylose ferromagnetic
propertiesandbehave like
paramagneticsubstances.

CONCEPT_MAP
using
Moving Charges

CONCEPT_MAP
Moving Charge and Force

QUESTIONS
MAGNETIC FORCE
1* In a certainarrangement,a proton does not get deflected while passing through a magnetic field
region. State the condition under which it is possible. 1
Ans: v is parallel or antiparallel to B
2 An electronbeamismovingverticallyupwards.If itpasses through a magnetic field directed from
South to North in a horizontal plane, in what direction will the beam be deflected? 1
Ans:-Towards geographical East in the horizontal plane
3 What is the work done by the magnetic force on a charged particle moving perpendicular to the
magnetic field? 1
Ans: Zero
4 A wire of length0.04m carrying a currentof 12 A isplacedinside asolenoid,makinganangle of 300
with its axis. The field due to the solenoid is 0.25 T. Find the force on the wire. 2
Ans; 0.06N
5 A circular loop of radius 0.1 m carries a current of 1A and is placed in a uniform magnetic field of
0.5T. The magneticfieldisperpendiculartothe plane of the loop.Whatis the force experiencedby
the loop? 2
Ans: The magnetic dipole does not experience any force in a uniform magnetic field.
Hence, the current carrying loop (dipole) does not experience any net force.
6* A proton, alpha particle and deuteron are moving in circular paths with same kinetic energies in
the same magnetic fields. Find the ratio of their radii and time periods.
Ans: Rp: Rα : Rd =1:1:√2 2
Tp: Tα : Td =1:2:2
7 An electronmovingwithKineticEnergy25 keV movesperpendiculartoa uniformmagneticfield of
0.2 mT. Calculate the time period of rotation of electron in the magnetic field. 2
Ans: T = 1.79 x 10-7
S
8 A charged particle of mass ‘m’ charge ‘q’ moving at a uniform velocity ‘v’ enters a uniform
magnetic field ‘B’ normal to the field direction. Deduce an expression for Kinetic Energy of the
particle.Whydoesthe KineticEnergyof the chargedparticle notchange whenmovingthroughthe
magnetic field? 3
9 An electronisrevolvingaroundthe nucleusof anatominan orbit of radius 0.53 Å. Calculate the
equivalent magnetic moment, if the frequency of revolution of the electron is 6.8 x 10 9
MHz.
Ans: pm = 9.6 x 10 -24
A m2
3
BIOT-SAVART LAW AND ITS APPLICATIONS
1 A current is set up in a long copper pipe. What is the magnetic field inside the pipe?
Ans: Zero 1
2 A wire placedalongnorth south direction carries a current of 5 A from South to North. Find the
magneticfielddue toa 1 cm piece of wire at a point 200 cm North East from the piece. 2
Ans: 8.8 x 10 -10
T, acting vertically downwards.
3 How will the magneticfiledintensityatthe centre of a circular coil carryingcurrentchange if the
current through the coil is doubled and the radius of the coil is halved. 2
Ans: B = μ0n x 2I / 2 x (R/2) = 4B
4 A circular coil of 500 turnshas a radiusof 2 m, and carriesa currentof 2 A. What isthe magnetic
fieldata pointon the axisof the coil at a distance equal toradiusof the coil from the center? 2
Ans: B = 1. 11 x 10 -4
T
5* The strength of magnetic induction at the center of a current carrying circular coil is B1 and at a
pointon itsaxisat a distance equal to its radius from the center is B2. Find B1/B2. 2
Ans: 2 √2
6* A current is flowing in a circular coil of radius ‘r’ and magnetic field at its center is B0. At what
distance from the center on the axis of the coil, the magnetic field will be B0/8? 2
Ans: x = √3r

7* A straightwire of length′
𝜋
2
′𝑚,isbentintoa circularshape.if the wire were tocarry a currentof
5 A,calculate the magneticfielddue toit,before bending,atapoint0.01 timesthe radiusof the
circle formedfromit.Alsocalculate the magneticfieldatthe centerof the circular loop formed,
for the same value of current. 3
Ans: B1 = 4 x 10 -4
T, B 2 = 1.256 x 10 -5
T
8 Two insulated wires perpendicular to each other in the same plane carry equal currents as
showninfigure.Isthere a regionwhere the magneticfieldis zero? If so, where is the region? If
not, explain why the field is not zero? 3
I
I
9 What is the net magnetic field at point 0 for the current distribution shown here?
ans (µ0 I / 2r)=(µoi/π r)
AMPERE’S CIRCUITAL LAW AND APPLICATIONS
1 A long straight solid metal wire of radius ‘R’ carries a current ‘I’, uniformly distributed over its
circularcross section.Findthe magneticfieldata distance ‘r’fromthe axisof the wire (a) inside
and (b) outside the wire 2
Ans; (a) µ0µrIr/2πR2
(b) µ02I/ 4πr
2 A solenoid is 1m long and 3 cm in mean diameter. It has 5 layers of windings of 800 turns each
and carriesa current of 5 A.FindMagnetic FieldInductionatthe centerof the solenoid. 2
Ans: 2.5 x 10 -2
T, parallel to the axis of the solenoid.
3 Findthe value of magneticfieldinside ahollow straight current carrying conductor at a distance
r from axis of the loop. 2
Ans B=0
FORCE BETWEEN TWO PARALLEL CURRENTS, TORQUE ON A CURRENT LOOP, MOVING COIL
GALVANOMETER
1* A rectangular loop of size 25 cm x 10 cm carrying a current of 15A is placed 2 cm away from a
long, straight conductor carrying a current of 25 A. What is the direction and magnitude of the
net Force acting on the loop?

Ans: F =7.8175 x 10-4
N
2* A long straight conductor PQ , carrying a current of 60 A, is fixed horizontally. Another long
conductor XY is kept parallel to PQ at a distance of 4 mm, in air. Conductor XY is free to move
and carries a current ‘I’ . Calculate the magnitude and direction of current ‘I’ for which the
magnetic repulsion just balances the weight of the conductor XY. 2
Ans:I = 32. 67 A,The currentin XY mustflow opposite tothatinPQ, because onlythenthe force
will be repulsive.
3 A circular coil of 200 turns, radius 5 cm carries a current of 2.5 A. It is suspended vertically in a
uniform horizontal magnetic field of 0.25 T, with the plane of the coil making an angle of 600
withthe fieldlines.Calculatethe magnitude of the torque thatmust be applied on it to prevent
it from turning. 2
Ans: 0.49Nm
4* A Galvanometer of resistance 3663 ohm gives full scale deflection for a certain current
Ig.Calculate the value of the resistance of the shuntwhichwhenjoinedto the galvanometer coil
will result in 1/34 of the total current passing through the galvanometer. Also find the total
resistance of the Galvanometer and shunt. 3
Ans: 111 ohm, 107.7 A.
MAGNETISM AND MATTER
BAR MAGNET
1 A shortbar magnethasmagneticmomentof 50 A m2
.Calculate the magneticfield intensity at a
distance of 0.2 m from its centre on (1) its axial line (2) its equitorial line. 2
Ans: B1 = 1.25 x 10 -3
T , B2 = 0.625 x 10 -3
T.
2 Calculate the torque acting on a magnet of length 20 cm and pole strength 2 x 10 -5
Am, placed
inthe earth’smagneticfieldof flux density2x 10 -5
T, when(a) magnetisparallel tothe field (b)
magnet is perpendicular to the field. 2
Ans: (a) Zero (b) 0.8 x 10 -10
Nm
MAGNETISM AND GAUSS LAW
1 What is the significance of Gauss’s law in magnetism? 1
Ans: Magnetic monopoles do not exist.
THE EARTH’S MAGNETISM
1 How the value of angle of dip varies on moving from equator to Poles? 1
2 A compass needle in a horizontal plane is taken to geographic north / south poles. In what
direction does the needle align? 1
3 The horizontal component of earth’s magnetic field is 0.2 G and total magnetic field is 0.4 G.
Find the angle of Dip. 1
Ans: 60. 250
4* A long straight horizontal table carries a current of 2.5 A in the direction 100
south of west to
10 0
north of east. The ,magnetic meridian of the place happens to be 10 0
west of the
geographic meridian. The earth’s magnetic field at the locations 0.33G and the angle of dip is
zero. Ignoring the thickness of the cable, locate the line of neutral points.
Ans: r = 1.5 cm ( BH = B cos δ, BH = µ0 I/ 2πr) 2
5 The vertical component of earth’s magnetic field at a place is √3 times the horizontal
component. What is the value of angle of dip at this place? 2
Ans: 600
6* A ship is sailing due west according to mariner’s compass. If the declination of the place is

150
east, what is the true direction of the ship? 2
Ans: 750
west of north.
IMPORTANT TERMS IN MAGNETISM
1 A magnetising field of 1600 A/m produces a magnetic flux of 2.4 x 10 -5
Wb in a bar of iron of
cross section 0.2 cm2
. Calculate permeability and susceptibility of the bar.
Ans: Permeability = 7.5 x 10-4
T A -1
m, Susceptibility =596.1 2
2 The maximum value of permeability of µ-metal is 0.126 Tm/A. Find the maximum relative
permeability and susceptibility.
Ans: 105
each. 2
MAGNETIC PROPERTIES OF MATERIALS
1 The susceptibilityof magnesiumat300K is 1.2 x 105
. At whattemperature will the susceptibility
be equal to 1.44 x 10-5
. 1
Ans: 250 K
2 An iron bar magnet is heated to 10000
C and then cooled in a magnetic field free space. Will it
retain its magnetism? 1
3 What is the net magnetic moment of an atom of a diamagnetic material? 1
Ans : Zero
4 Which materials have negative value of magnetic susceptibility? 1
Ans : Diamagnetic materials.
5 Why permanent magnets are made of steel while the core of the transformer is made of soft
iron? 1
6* An iron rod of volume 10-4
m3
and relative permeability 1000 is placed inside a long solenoid
wound with 5 turns/cm. If a current of 0.5A is passed through the solenoid , find the magnetic
moment of the rod. 2
7* The susceptibilityof amagnticmateial is0.9853. Identifythe type of the magneticmaterial.Draw
the modificationof the field pattern on keeping a piece of this material in a uniform magnetic
field. 2
Ans : paramagnetic
8 Two similar bars, made from two different materials P and Q are placed one by one in a non
uniform magnetic field. It is observed that (a) the bar P tends to move from the weak to the
strongfieldregion.(b) the barQ tendstomove fromthe strongto the weakfieldregion.Whatis
the nature of the magnetic materials used for making these two bars? 2
4. ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS
GIST
1 The phenomenoninwhichelectric current is generated by varying magnetic fields is called
electromagnetic induction.
2 Magneticflux througha surface of area A placed in a uniform magnetic field B is defined as
ΦB = B.A = BACosθ where θ is the angle between B and A.
3 Magneticflux isa scalar quantityandits SIunitis weber(Wb). Itsdimensional formulais[Φ]
= ML2
T-2
A-1
.
4 Faraday’s laws of induction states that the magnitude of the induced e.m.f in a circuit is
equal to the time rate of change of magnitude flux through the circuit.

ε= −
𝑑∅ 𝐵
𝑑𝑡
5 Accordingto Lenzlaw,the directionof inducedcurrentorthe polarityof the inducede.m.f is
such that ittendsto oppose the change inmagneticflux thatproduces it. (The negative sign
in Faraday’s law indicates this fact.)
6 Lenz law obeys the principle of energy conservation.
7 The inducede.m.f canbe producedby changingthe (i) magnitude of B(ii) area A (iii) angle θ
between the direction of B and normal to the surface area A.
8 Whena metal rod of lengthl isplaced normal toa uniformmagneticfield B and moved with
a velocityvperpendicular to the field, the induced e.m.f is called motional e.m.f produced
across the ends of the rod which is given by ε = Blv.
9 Changing magnetic fields can setup current loops in nearby metal bodies (any conductor).
Such currents are called eddy currents. They dissipate energy as heat which can be
minimized by laminating the conductor.
10 Inductance is the ratio of the flux linkage to current.
11 When a current in a coil changes it induces a back e.m.f in the same coil. The self induced
e.m.f is given by ε = −𝐿
𝑑𝐼
𝑑𝑡
where L is the self-inductance of the coil. It is a measure of
inertia of the coil against the change of current through it. Its S.I unit is henry (H).
12 A changing current in a coil can induce an e.m.f in a nearby coil. This relation,
ε = −𝑀12
𝑑𝑖2
𝑑𝑡
, shows that Mutual inductance of coil 1 with respect to coil 2 (M12) is due to
change of current in coil 2. (M12 = M21).
13 The self-inductance of a long solenoid is given by L = µ0n2
Al where A is the area of cross-
section of the solenoid, l is its length and n is the number of turns per unit length.
14 The mutual inductance of two co-axial coilsisgivenbyM12 = M21 = µ0 n1n2Al where n1&n2 are
the number of turns per unit length of coils 1 & 2. A is the area of cross-section and l is the
length of the solenoids.
15 Energy stored in an inductor in the form of magnetic field is 2
max
1
2
BU Li and
Magnetic energy density
0
2
2B
B
U


16 In an A.C. generator, mechanical energy is converted to electrical energy by virtue of
electromagnetic induction.
* Rotationof rectangularcoil ina magneticfieldcauseschange influx (Φ= NBACosωt).
* Change in flux induces e.m.f in the coil which is given by
ε= -dΦ/dt = NBAωSinωt ε 𝜀= ε0Sinωt
* Current induced in the coil I = ε/R = ε0Sinωt/R = I0Sinωt
17 An alternating voltage ε=ε0Sinωt, applied to a resistor R drives a current I = I0Sinωt in the
resistor,I0 = ε0 /Rwhere ε0&I0 are the peakvaluesof voltage andcurrent.(alsorepresentedby
Vm & Im)
18 The root mean square value of a.c. may be defined as that value of steady current which
would generate the same amount of heat in a given resistance in a given time as is done by
the a.c. when passed through the same resistance during the same time.
Irms = I0/√2 = 0.707i0

Similarly, vrms = v0/√2= 0.707v0.
For an a.c. ε = εm Sin ωt applied to a resistor, current and voltage are in phase.
19 In case of an a.c. circuit having pure inductance current lags behind e.m.f by a phase angle
90°. ε = εm Sin ωt and i = im Sin (ωt-Π/2)
Im = εm/XL; XL = ωL is called inductive reactance.
20 In case of an a.c. circuithaving pure capacitance, current leads e.m.f by a phase angle of 90°.
ε = εmSinωt and I= ImSin(ωt+π/2) where
Im = εm/XC and XC = 1/ωC is called capacitive reactance.
21 In case of an a.c. circuit having R, L and C, the total or effective
resistance of the circuit is called impedance (Z).
Z = εm / Im = 2
LC
2
)X-(X+R
tanΦ =
c LX X
R

where φ is the phase difference
between current and voltage.
ε = εmSinωt, I= ImSin(ωt+Φ)
23 Average power loss over a complete cycle in an LCR circuit is
P = εrmsIrmsCosΦ
* In a purely resistive circuit Φ = 0; P = VRMSIRMS.
* In a purely inductive circuit Φ = Π/2; P = 0.
* In a purely capacitive circuit Φ = Π/2; P = 0.
24 In an LCR circuit, the circuit admits maximum current if XC = XL, so that Z = R and resonant
frequency 𝜔 𝑟 =
1
√ 𝐿𝐶
𝑎𝑛𝑑 𝜗 𝑅 =
1
2𝜋√ 𝐿𝐶
25 Q factor of series resonant circuit is defined as the ratio of voltage developed across the
inductance or capacitance at resonance to the applied voltage across ‘R’,
Q=
𝜔 𝑟 𝐿
𝑅
𝑜𝑟
1
𝜔 𝑟 𝐶𝑅
also 𝑄 =
𝜔 𝑟
2∆𝜔
where 2∆𝜔 is bandwidth.
26
for a transformer,
ps s
p p s
iE N
K
E N i
  
In an ideal transformer, εPIP = εSIS. i.e
If NS>NP; εS>εP& IS<IP – step up. If NP>NS; εP>εS & IP<IS – step down.
27 A circuitcontaining an inductor L and a capacitor C (initially charged) with no a.c. source and
no resistors exhibits free oscillations of energy between the capacitor and inductor. The
charge q satisfies the equation
2
2
1
0
d q
q
LCdt
 

CONCEPT MAP
EMI and application

QUESTIONS
MAGNETICFLUX, INDUCED E.M.F,
1 Two concentric circular coils are perpendicular to each other. Coil I carries a current i. If this
current is changed, will this induce a current in the coil II?
[No- Field due to one coil is parallel to the plane of the second coil. So
flux does not change.]
1
2 A closedloopof wire isbeing moved with constant velocity without changing its orientation
inside a uniform magnetic field. Will this induce a current in the loop?
[Ans:No there isnochange inΦB]
1
3 A cylindrical barmagnetiskeptalong the axis of a circular coil and near it as shown in the fig.
Will there be any induced current at the terminals of the coil when the magnet is rotated a)
about its own axis b) about an axis perpendicular to the length of the magnet?
N S
Fig(i) Fig(ii)
AnsFig.(i) Noe.m.f will be induced,asthese isnochange influx.
Fig(ii) Yes,Φ changescontinuously.Soe.m.f isinducedinthe coil.
1
4 A conductingwire iskeptalongthe N→Sdirectionandisallowedtofall freely.Will ane.m.f
be inducedinthe wire?
(Yes)
1
5 A conductingwire iskeptalongthe E→Wdirectionandisallowedtofall freely.Will ane.m.f
be inducedinthe wire?
(Yes)
1
6 A vertical magneticpole fallsdownthroughthe plane of magneticmeridian.Will anye.m.f be
inducedbetweenitsends?
Ans:No,because the pole interceptsneitherBv orBH
1
II
I

7 A wheel withacertainnumberof spokesisrotatedina plane normal toearth’smagneticfield
so that an emf isinducedbetweenthe axle andrimof the wheel,keepingall otherthings
same, numberof spokesischanged.How isthe e.m.f affected?
(Hint:Numberof spokesdoesnotaffectthe netemf)
1
8 What are eddycurrents? 1
9 Explainanytwoapplicationsof eddycurrent. 2
10 The magneticflux linkedwithacoil passingperpendiculartothe plane of the coil changeswith
time Φ = 4t2
+ 2t + 3, where “t” isthe time inseconds. What is magnitude of e.m.f inducedat
t = 1 second?
Ans:(e = dΦ/dt =  2
4 2 3
d
t t
dt
  ,e = 8t +2 If t = 1s e= 10V)
3
11 A wheel fittedwithspokesof radius‘r’isrotatingat a frequencyof nrevolutions persecond
ina plane perpendiculartomagneticfieldBTesla.Whatisthe e.m.f inducedbetweenthe axle
and rimof the wheel?
[2]
Φ = BA
e = d(BA)/dt=B dA/dt,dA/dt=Πr2
x n
e = B. Πr2
n
3
12 Two coilsP andS are arrangedas showninthe figure.
(i) What will be the directionof inducedcurrentinSwhenthe switchisclosed?
(ii) Whatwill be the directionof inducedcurrentinSwhenthe switchisopened?
Ans:(i) anticlockwise (ii) clockwise
2
13 A conducting circular loop is placed in a uniform magnetic field B = 0.020T with its plane
perpendiculartothe field.Somehow,the radiusof the loop starts shrinking at a constant rate
of 1mm/s. Find the induced current in the loop at an instant when the radius is 2cm.
Ans. (Ф= Πr2
B d Ф/dt = 2ΠrB dr/dt e= 25μV
2
14 A 12V batteryisconnectedtoa 6Ω; 10 H coil througha switchdrivesaconstant current in the
circuit.The switchis suddenlyopened.Assuming thatittook1ms to open the switch calculate
the average e.m.f induced across the coil.
Ans.(Iinitial=2A I final=0 𝜀=-Ldi/dt = 20000V)
2
15 A coil of mean area 500 cm2
having 1000 turns is held perpendicular to a uniform magnetic
fieldof 0.4 G. The coil isturnedthrough180 o
in 1/10 seconds.Calculate the average induced
e.m.f.
Ans.(0.04 V)
2
S
P

16 A conductingrodof lengthl withone endpivotedisrotatedwithauniformangularspeedω
ina Vertical plane normal touniformmagneticfieldB.Deduce anexpressionfore.m.f induced
inthisrod.
2
17 Two identical co-axial coilscarryequal currents.Whatwill happento the current in each loop
if the loops approach each other?
(2)
Ans.(Acc to Lenz’slawcurrentineach coil will decrease)
2
18 Obtainthe directionof inducedcurrentande.m.f whenthe conductorABismovedat right
anglestoa stationarymagneticfield(i) inthe upwarddirection(ii) inthe downwarddirection.
(i) B to A (ii) A to B)
2
19 A fan blade of length0.5 m rotatesperpendiculartoa magneticfieldof 5x10 -5
T. If the e.m.f
inducedbetweenthe centre andthe endof the blade is10 -2
V . Findthe rate of rotation.
Ans.(e=BdA/dt; dt= 1/n ; n=254.7 rev/s)
3
20 The figure shows a square loop having 100 turns an area of 2.5x10 -3
m2
and a resistance of
100Ώ . The magneticfieldhasamagnitude of B= 0.4 T. Findthe work done in pulling the loop
out of the field slowly and uniformly in 1 second.
P Q R
* * * * * * *
* * * * * *
* * * * * * *
Alsodrawgraph showingthe variationof power deliveredwhenthe loopismovedfromPto Q
to R. (1x 10-6
J)
3
21 Two coils have a mutual inductance of 0.005H. The current changes in the first coil according
to the equation I= I0 Sin ωt where I0 =10A and ω=100∏ rad/s. Calculate the maximum value
of e.m.f in the second coil. (5 π volts)
3
22 A longrectangularconductingloopof width L mass m and resistance R is placed partly above
and partlybelowthe dottedline withthe loweredge paralleltoit.Withwhatvelocityitshould
continue to fall without any acceleration?
3
G
N
S
A
B
v

* * * * * * * * *
* * * * * * * * *
-*--*--*----------*---*----
(mg = B2
l2
v/r ; v=mgr/ B2
l2
)
INDUCTANCE
1 Two conductingcircularloopsof radii R1 andR2 are placedinthe same plane withtheir
centrescoinciding.Findthe mutual inductance betweenthemassumingR2<<R1.
(M=µ0 πR2
2
/2R1)
2
2
Prove that the total inductance of two coilsconnectedinparallelis
1 2
1 1 1
TL L L
 
2
3 Two circularloopsare placedwiththeircentresatfixeddistanceapart.How wouldyou
orientthe loopstohave (i) maximum (ii) minimumMutual inductance?
2
4 A coil of wire of certain radius has 600 turns and inductance of 108mH. What will be the
inductance of another similar coil with 500 turns? (75mH)
2
5 Obtainthe mutual inductance of a pairof coaxial circularcoilskeptseparatedbya distance
as showninfig:-
2
ALTERNATING CURRENT - RMS CURRENT AND VOLTAGE
1 Find the RMS value of A.C shown in the figure. 1
R
r

2 The instantaneous value of e.m.f is given by ε= 300sin 314t. What is the rms value of emf ?
Ans:- 𝜀0=300 units 𝜀rms=212.1 units
1
3 Why a 220 V AC is considered to be more dangerous than 220 V DC?
Ans:peakvalue of AC ismore than rms value whichisequal to311V.
1
4 An ACcurrent flowsthroughacircuitconsistingof differerentelements connected in series.
(i) Is the applied instantaneous voltages equal to the algebraic sum of instantaneous
voltages across the series elements of the circuit? (ii) Is it true for rms voltages?
Ans: (i) yes (ii) no
1
5 A capacitor blocks DC. Why?
Ans: XC=1/(2πfC ), for D.C f=0, therefore Xc=∞
1
6 What isthe phase relationshipbetweene.m.f acrossL andC in a seriesLCRcircuit connected
to an A.C source?
Ans:-The phase difference betweenVL andVC=1800
1
7 Two alternating currents are given by I1=I0Sinωt and I2= I0Sin(ωt+π/3). Will the rms value
ofI1 & I2 be equal or different?
Ans:The rms value will be equal.
1
8 An alternatingcurrentisgivenbyi=i1Cosωt+i2Sin ωt. Find the rms current in the circuit. (2)
Ans:√
( 𝑖1
2+𝑖1
2)
2
2
9 An alternating current having a peak value of 14A is used to heat a metal wire. What is the
value of steady current which can produce the same heating effect as produced by AC?
Why? Ans: irms=10A
2
10 If a constantcurrent of 2.8A exists in a resistor, what is the rms value of current? Why? (2)
Ans: 2.8A
2
11 Sketch a graph showingthe variation of impedanceof LCR circuitwith the frequency of applied
voltage. (1)
1
12 If resistance Rincircuit‘a’ be decreased,whatwill be the directionof inducedcurrentinthe
circuit‘b’.
2
Z
ϑϑr

AC CIRCUITS
1 What ismeantby wattlesscurrent? 1
2 Define:Qfactorin LCR seriescircuit 1
3 Why ischoke coil preferredoverresistortoreduce a.c? 1
4 How doR, XL and XC getaffectedwhenthe frequency of applied AC is doubled?
Ans: a) R remains unaffected
b) XL=2πfL, so doubled
c) XC=1/2πfC, so halved
3
5 For circuits for transporting electric power, a low power factor implies large power loss in
transmission line. Why?
(2)
Ans: rms
rms
P
i
V Cos

2
6 In an AC circuit there is no power consumption in an ideal inductor. Why?
Ans: P= Vrms Irms Cos π/2 =0
2
7 An LCR series circuit is connected to an AC source. Which of its components dissipates
power?
L or C or R? Justify your answer.
Ans:Resistance,PowerinLand C = 0
2
8 An electric lamp connected in series with a capacitor and an AC source is glowing with
certain brightness. How does the brightness of the lamp change on reducing the
capacitance?
Ans:Brightnessdecreases.(AsCdecreases,XC increases.Hence Zincreasesand Idecreases.)
2
9 The power factor of an AC circuit is lagging by a factor 0.5. What does it mean? (2)
Ans:CosФ=0.5, ie,Ф =600
. Thisimpliesthatthe currentlagsbehindappliedvoltage bya
phase angle of 600
2
10 The peakvalue of an ACis 5A and itsfrequencyis60Hz. Finditsrms value.How long will the
current take to reach the peak value starting from zero?
Ans: Irms= 3.5A . Time period T=(1/60)s . The current takes one fourth of the time period to
reach the peak value starting from zero. t =T/4 =(1/240)s.
2
11 The voltage andcurrent ina seriesACcircuitare given by V= V0 Cosωt & I= I0 Sinωt. What is
the power dissipated in the circuit?
Ans:- I=I0Sinωt & V=V0Sin(ωt+π/2), since V leads current by a phase angle π/2, it is an
inductive circuit . So, P=0
2
12 Whenan AC source isconnectedtoa capacitorwitha dielectricslab between its plates, will
the rms current increase or decrease or remain constant?
Ans: The capacitance increases, decreasing the reactance Xc . Therefore the rms current
increases.
2
13 Can peak voltage across an inductor be greater than the peak voltage supplied to an LCR? 2

Ans: Yes, at the time of break of a circuit, a large back e.m.f is set up across the circuit.
14 Write any twodifferencesbetweenimpedance andreactance. 2
15 A 100 Ω resisterisconnectedto220V, 50 cyclesperseconds.Whatis (i) peakpotential
difference (ii) average potentialdifference and(iii) rmscurrent?
Ans. 𝜀o=311.08V, 𝜀m =197.9V, Iv= 2.2 A
2
16 Define and derive the root mean square value of a.c voltage 3
RESONANCE in LCRCircuits
1 An inductor of inductance 100mH is connected in series with a resistance, a variable
capacitance and an AC source of frequency 2 kHz. What should be the value of the
capacitance so that maximum current may be drawn into the circuit?
Ans:1/ωC=ωL ; C=1/ω2
L=63nF.
2
2 In the circuit shown below R represents an electric bulb. If the frequency of the supply is
doubled,howthe valves of C and L should be changed so that the glow in the bulb remains
unchanged?
Hint: XL=2πfL XC=1/2πfC
2
3 Draw phasordiagram foran LCR circuitforthe cases(i) the voltage acrossthe capacitor is
greaterthan that acrossthe inductor(ii) voltage acrossinductorisgreaterthanthatacross
the capacitor.
2
4 Doescurrent inAC circuitlag,leador remaininphase withvoltage of frequency υ applied to
a series LCR circuit when (i) υ = υ r
(ii) υ< υr (iii) υ> υr, where υr resonantfrequency?
1
5 11kw of electricpowercanbe transmittedtoa distantstationat (i) 220V and(ii) 22kV.
Whichof the two modesof transmission shouldbe preferredandwhy?
2
6 In an AC circuit V and I are given by V=100Sin100t volts and I= 100 Sin(100t+π/3)mA
respectively. What is the power dissipated in the circuit?
Ans: V0=100V I0=100A Ф= π/3 P=Vrms Irms Cos Ф=2500W
2
7 The potential across a generator is 125V when it is suppling10A. When it supplies 30A, the
potential is 120V. What is the resistance of the armature and induced e.m.f?
Ans:E=127.5V
2
8 In an LCR circuit the potential difference between terminals of inductance 60V, between
terminals of capacitor 40V and between the terminals of resistor is 40V. Find the supply
voltage. (3)
Ans: InseriesLCRcircuit voltage acrosscapacitorand inductor are in opposite phase, so net
voltage across the combination of L and C becomes 60-30=30V. Total voltage across R and L
= 50V
3

9 The natural frequency of an LC circuit is 1,25,000 Hz. Then the capacitor C is replaced by
another capacitor with a dielectric medium k, which decreases the frequency by 25 KHz.
What is the value of k?
Ans: υ1=1/2π√LC υ2=1/2π√kLC k=( υ1/ υ2)2
=(1.25)2
=1.56.
3
10 Obtainthe resonant frequency and Q factor of a series LCR circuit with L= 3H, C= 27µF and
R= 7.4 Ώ. Write two different ways to improve quality factor of a series LCR circuit
Ans: Q=45,ω0=111rad/s
3
11 An A.C source of voltage V= Vm Sinωt is connected one-by-one to three circuit elements
X, Y and Z. It is observed that the current flowing in them
i. is in phase with applied voltage for X
ii. Lags applied voltage in phase by π /2 for elements Y.
iii. Leads the applied voltage in phase by π /2 for element Z.
Identify the three circuit elements.
5
TRANSFORMER
1 Why isthe core of a transformerlaminated? 1
2 Why can’t a transformerbe usedtostepup dc voltages? 1
3 The graph belowshowsthe variationof Iwitht. If it isgiventothe primaryof a transformer,
whatis the nature of inducede.m.f inthe secondary?
(Hint:e has constant positive value inthe firstpartanda constantnegative value in the
secondpart)
1. The turn ratio of a transformeris10. What isthe e.m.f inthe secondaryif 2V is supplied
to primary?
2. A transformerhasan efficiencyof 80% It worksat 4kW and 100V. If the secondaryvoltage
Is240V findthe primarycurrent.
(40 A )
3
4 Whena voltage of 120V is giventothe primaryof a transformerthe currentinthe primaryis
1.85mA. Findthe voltage acrossthe secondarywhenitgivesacurrentof 150mA. The
efficiencyof the transformeris95%
(1406V)
3
I
t

GENERATOR
1 If the speedof rotationof armature isincreasedtwice how woulditaffectthe (a) maximum
e.m.f produced(b) frequencyof the e.m.f?
(e=NBAω;f=ω/2Π)
1
2 A coil of area 0.2m2
and 100 turnsrotatingat 50 revolutionspersecondwiththe axis
perpendiculartothe field.If the maximume.m.f is7kV determine the magnitude of
magneticfield. (1.1 Tesla)
2
3 An ac generatorconsistsof a coil of 50 turnsand an area of 2.5m2
rotatingat an angular
speedof 60 rad/sin a uniformmagneticfieldof B=0.3T betweentwofixedpole pieces.The
resistance of the circuitincludingthatof the coil is500Ώ
(i) What isthe maximumcurrentdrawnfromthe generator?
(ii)Whatisthe flux throughthe coil whencurrentiszero?
(iii)Whatisthe flux whencurrentismaximum?
(4.5A,375Wb, zero)
3
5. ELECTRO MAGNETIC WAVES
GIST
1. Conduction current and displacement current together have the property of continuity.
2. Conduction current & displacement current are precisely the same.
3. Conduction current arises due to flow of electrons in the conductor. Displacement current arises
due to electric flux changing with time.
4. 𝑰 𝑫 = 𝜺 𝟎∫
𝒅∅ 𝑬
𝒅𝒕
5. Maxwell’s equations
 Gauss’s Law in Electrostatics
∮ 𝐸⃗⃗. 𝑑𝑆⃗⃗⃗⃗⃗=
𝑄
𝜀0
 Gauss’s Law in Magnetism
∮ 𝐵⃗⃗. 𝑑𝑆⃗⃗⃗⃗⃗=0
 Faraday’s -Lenz law of electromagnetic induction.
∮ 𝐸⃗⃗ . 𝑑𝑙⃗⃗⃗⃗=∫
𝐵⃗⃗
𝑑𝑡
.𝑑𝑆⃗⃗⃗⃗⃗
 Ampere’s – Maxwell law
∫ 𝐵⃗⃗ . 𝑑𝑙⃗⃗⃗⃗ =0 I + 0 0∫
𝐸⃗⃗
𝑑𝑡
. 𝑑𝑆⃗⃗⃗⃗⃗
6. ElectromagneticWave :- The wave inwhichthere are sinusoidal variation of electric and magnetic
field at right angles to each others as well as right angles to the direction of wave propagation.
7. Velocity of EMwaves in free space:𝑐 =
1
√ 𝜇0𝜀0
3x108
m/s
8. The Scientists associated with the study of EMwaves are Hertz,
Jagdish Chandra Bose & Marconi.
9. EM wave is a transverse wave because of which it undergoes polarization effect.
10. Electric vectors are only responsible for optical effects of EMwaves.
11. The amplitude of electric & magnetic fields are related by
𝐸
𝐵
= 𝑐
12. Oscillating or accelerating charged particle produces EMwaves.

13. Orderly arrangement of electro magnetic radiation according to its frequency or
wavelength is electromagnetic spectrum.
14. Hint to memorise the electromagnetic spectrum in decreasing order of its frequency.
Gandhiji’s X-rays Used Vigorously InMedical Research
15. EM waves also carry energy, momentum and information.
ELECTRO MAGNETIC SPECTRUM, ITS PRODUCTION, DETECTION AND USES IN GENERAL
Type
Wave length Range
Frequency Range
Production Detection Uses
Radio >0.1m
109
to 105
Hz
Rapid acceleration
/ deceleration of
electrons in aerials
Receiver’saerials Radio, TV
Communication
Microwave
0.1mm
1011
to109
Hz Klystron valve or
magnetron valve
Point contact
diodes
Radar, TV
communication
Infrared
1mm to 700nm
1011
to1014
Hz Vibration of atom
or molecules
Thermopiles,
Bolometer
Infrared
Photographic
Film
Green House effect,
lookingthrough haze,
fog and mist, Ariel
mapping.
Light
700nm to 400nm
8x1014
Hz Electronin an atom
during transition
Eye, Photocell,
Photographic
Film
Photography,
Illuminations, Emit &
reflectbythe objects.
Ultraviolet
400nm to 1nm
5x1014
to 8x1014
InnerShell electron
in atom moving
from one energy
level to a lower
energy level
Photocell &
photographic
film
Preservation of food
items, Detection of
invisible writing,
fingerprintinforensic
laboratory.
Determination of
Structure of
molecules & atoms.
X-rays
1nm to 10-3
nm
1016
to 1021
Hz
X-ray tube or inner
shell Electrons
Photographic
film, Geiger
tube, ionization
chamber.
Study of crystal
structure & atom,
fracture of bones.
Gamma ray
<10-3
nm
1018
to 1022
Hz
Radioactive decay
of the nucleus Photographic
film, Geiger
tube, ionization
chamber
Nuclear reaction &
structure of atoms &
Nuclei.
To destroy cancer
cells.

CONCEPT MAP
Electromagnetic Waves

QUESTIONS
1. Write the SI unit of displacement current? 1
Ans : Ampere
2. If 𝐸⃗⃗, 𝐵⃗⃗represent electric and magnetic field vectors of the electromagnetic waves,
then what is the direction of propagation of the electromagnetic wave? 1
Ans: 𝐸⃗⃗ × 𝐵⃗⃗
3. Can the velocity of light in vacuum be changed? 1
Ans: Not possible
4 Calculate the wavelength of EMW emitted by the oscillator antenna system, if L=
0.253 µH & C = 25Pf ? 1
Ans 1
2𝜋√ 𝐿𝐶
5. The magnetic component of polarized wave of light is
𝐵 𝑋 = (4 × 10−6 𝑇)Sin [(1.57 × 107 𝑚−1) 𝑦 + (4.5 × 1011 𝑡)]
(a) Find the direction of propagation of light
(b) Find the frequency
(c) Find intensity of light
3
Ans Y axis
f = (4.5 x 10 11
)/2π Hz
I ∝ A2
6. What physical quantity is same for X-rays of wavelength 10-10
m, red light of
wavelength 6800 Å and radio wave of wavelength 500 m? 1
Ans Velocity
7. The amplitude of 𝐵⃗⃗of harmonicelectromagnetic wave in vacuum is Bo=510 n T. What
is the amplitude of the electric field part of the wave? 1
Ans 153 N/C
8. Suppose Eo =120 N/C and its frequency  = 50Hz. Find Bo, ω, k and  and write
expression for E and B ? 2
Ans 𝐸⃗⃗ 𝑦 = 120 𝑆𝑖𝑛[1.05𝑥 − 3.14 × 108 𝑡] 𝑗̂NC-1
𝐵⃗⃗𝑍 = 400 𝑆𝑖𝑛[1.05𝑥 − 3.14 × 108 𝑡] 𝑘̂nT
Bo = 400 n T ; ω = 108
rad/s, k=1.05 rad/m ,  = 6m
9. The charging current for a capacitor is 0.25 A. what is the displacement current across
its plates?
1
Ans 0.25 A
10. A variable frequency a.c source is connected to a capacitor. Will the displacement
current increase or decrease with increasing frequency? 1
Ans Increases

11. EMW travel in a medium at a speed of 2x108
m/s. the relative permeability of the
medium is 1.0. Calculate the relative permittivity?
Ans r = 2.25
rr
C
V
 

12. How does a charge q oscillating at certain frequency produce electromagnetic wave?
1
Ans Oscillating charge produces oscillating E which produces oscillating B and so on
13. How would you establish an instantaneous displacement current of 1A in the space
between the parallel plates of 1µF capacitor? 1
Ans By changing the voltage dv/dt =106
V/s
14. Name the Maxwell’s equation among the four which shows that the magnetic
monopole does not exist? 1
Ans Gauss’s theorem of Magnetism
15. Write the unit of µoo? 1
Ans (m/s)-2
16. Give reason for decrease or increase in velocity of light, when it moves from air to
glass or glass to air respectively? 1
Ans The velocity of light depends on ε & μ of the medium.
17. A parallel plate capacitor made of circular plates each of radius 10 cm has a
capacitance 200pF. The capacitor is connected to a 200V a.c. supply with an angular
frequency of 200 rad/s.
a) What is the rms value of conduction current
b) Is the conduction current equal to displacement current
c) Peak value of displacement current
d) Determine the amplitude of magnetic field at a point 2cm from the axis
between the plates
2
Ans a) Irms = 8µA
b) Ic = Id
c) Io =21/2
Irms
B = 4.525  10-12
T
18. Electromagnetic waves with wavelength
(i)
1
 , are used to treat muscular strain.
(ii)
2
 , are used by a FM radio station for broadcasting..
(iii)
3
 , are produced by bombarding metal target by high speed electrons.
(iv)
4
 , are observed by the ozone layer of the atmosphere.
Identify and name the part of electromagnetic spectrum to which these radiation
belong. Arrange these wave lengths, in decreasing order of magnitude.
3
Ans
1
 Infra red radiation.
2
 VHF / Radiowaves.
3
 X – rays
4
 UV
2
 >
1
 >
4
 >
3

6. OPTICS
RAY OPTICS
GIST
19. a) Which of the following if any, can act as a source of electromagnetic waves.
(i) A charge moving with constant velocity.
(ii) A charge moving in circular orbit.
(iii)A charge at rest. Give reason
(b) Identify the part of electromagnetic spectrum to which the waves of frequency
(i) 1020
Hz (ii) 109
Hz belong.
3
Ans a) Can’t produce em waves because no accelration.
(ii) It is accelrated motion - can produce em waves.
(iii)Can’t produce em waves because no accelration.
b) (i) Gamma rays.
(ii) Micro waves
1 REFLECTION BY CONVEX AND CONCAVE MIRRORS.
a.Mirror formula
fuv
111
 , where u is the object distance, v is the image
distance and f is the focal length.
b.Magnification
uf
f
f
vf
u
v
m



 .
m is -ve for real images and +ve for virtual images.
2 REFRACTION
c. Ray of light bends when it enters from one medium to the other, having
different optical densities.
d. Sun can be seen before actual sunrise and after actual sunset due to
Atmospheric refraction
e. An objectunderwater( any medium ) appears to be raised due to refraction
when observed inclined
Real depth
n
apparent depth
 and
Shift in the position (apparent) of object is
X = t { 1 – 1/n) where t is the actual depth of the medium
f. Snell’slawstates thatfora given colour of light, the ratio of sine of the angle
of incidence tosine of angle of refraction is a constant, when light travels from
rarer to denser,
2
1sin
nSini
r n

g. Absolute refractive index is the ratio between the velocities of light in
vacuum to the velocity of light in medium. For air n=1.
c
n
v

3 h.When a ray of light travels from denser to rarer medium and if the angle of
incidence is greater than critical angle, the ray of light is reflected back to the

denser medium. This phenomenon is called Total internal reflection.
D
R
n
n
SinC 
i. Diamond has a high refractive index, resulting with a low critical angle
(C=24.40
). Thispromotesa multiple total internal reflectioncausingitsbrilliance
and luster.Some examples of total internal reflection are formation of mirage
and working of an optical fibre.
4 Whenlightfallsona convex refractingsurface,itbendsandthe relation
betweenU,V and R is givenby 2 1 2 1n n n n
V u R

 
5 Lens maker’s formula or thin lens formula is given by
2 1
1 1 2
1 1 1n n
f n R R
  
   
  
For Convex Lens R1 +ve ;R2 –ve Concave lens R1-ve; R2 +ve
The wayin whicha lensbehavesas converging or diverging depends upon the values
of nL and nm.
6 When two lenses are kept in contact the equivalent focal length is given by
21
21
PP&
111
P
ffF

7
The lens formula is given by
fuv
111

8. When light passes through a glass prism it undergoes refraction.
The expression for refractive index is
2
2
mA D
Sin
n
A
Sin
 
 
 
 
 
 
As the angle of incidence increases, the angle of deviation decreases, reaches a
minimumvalue and then increases. This minimum value is called angle of minimum
deviation “Dm”.
9
where d is minimum, i=e, refracted ray lies
parallel to the base. For a small angled prism d=(n-1)A
10 Whenwhite light(polychromaticorcomposite) ispassedthroughaglassprism, It
Q
U
d

QUESTIONS
REFLECTION
splitsupintoits componentcolours(Monochromatic).Thisphenomenoniscalled
Dispersion.
11m. Rainbow is formed due to a combined effect of dispersion, refraction and
reflection of sunlight by spherical water droplets of rain.
12 Scattering of light takes place when size of the particle is very small when
compared to the wavelength of light
Intensity of scattered light is 4
1
I

The following properties or phenomena can be explained by scattering.
(i) Sky is blue.
(ii) Sky is reddish at the time of sunrise and sunset
(iii) Infra-red photography used in foggy days.
(iv) Orange colour of black Box
(v) Yellow light used in vehicles on foggy days.
(vi) Red light used in signals.
1 One half of the reflectingsurface of aconcave mirroris coatedwithblackpaint. How
will the image be affected?
Brightnessdecreases
2 Why a concave mirror is preferred for shaving?
Enlarged VIRTUAL
3 Mirrors in search lights are parabolic and not spherical. Why?
Produce intense parallel beam) eliminating spherical aberration
4 Usingthe mirrorformulashowthat a virtual image isobtainedwhenan object is placed
in between the principal focus and pole of the concave mirror.
1 1 1 1 1
u<f is +vev
v u f u f
     )
5 Usingthe mirrorformulashowthat fora concave mirror,whenthe objectisplacedat
the centre of curvature,the image isformedatthe centre of curvature.
6 Find the position of an object, which when placed in front of a concave mirror of focal
length 20cm, produces a virtual image which is twice the size of the object.
Ans. 10cm
7 Plot a graph between 1/u and 1/v for a concave mirror. What does the slope of the
graph yield?
Ans. Straight line, slope =u/v=1/m

8 REFRACTION AND LENSES
Whichof the followingpropertiesof light:Velocity,wavelengthandfrequency,changes
duringthe phenomenon(i)reflection(ii) refraction
Ans. (i) No change (ii) velocity, wavelength change)
9 A convex lensiscombinedwithaconcave lens.Draw a ray diagramto show the image
formedbythe combination,foranobjectplacedinbetweenf and2f of the convex lens.
Compare the Powerof the convex andconcave lensessothat the image formedisreal.
Ans:f of convex lensmustbe lessthanf of concave lenstoproduce real image.So
powerof Convex greaterthanthat of concave)
10
Derive a relation between the focal length and radius of curvature of a Plano convex
lens made of glass. Compare the relation with that of a concave mirror. What can you
conclude? Justify your answer.
Ans. (f=2R) both are same. But applicable always in mirrors, but for lenses only in
specific cases, the relation can be applied.)
11 In the given figure an object is placed at O in a medium (n2>n1). Draw a ray diagram for
the image formation and hence deduce a relation between u, v and R
1 2 1 2n n n n
v u R

 
12 Showthat a concave lensalwaysproduces avirtual image,irrespectiveof the positionof
the object.
Ans.
-ve. that is virtual
uf
v But u is ve and f is ve for concave lens
u f
Hence v is always
  

13 Sun glasses are made up of curved surfaces. But the power of the sun glass is zero.
Why?
Ans. It is convex concave combination of same powers. So net power zero
14 A convex lensisdifferentiatedtonregionswithdifferentrefractiveindices.How many
imageswill be formedbythe lens?
Ans.n imagesbutlesssharp
15
A convex lenshasfocal lengthf inair.What happens to the focal length of the lens, if it
is immersed in (i) water (n=4/3) (ii) a medium whose refractive index is twice that of
glass.
Ans. 4f, -f
16 Calculate the critical angle forglassair surface,if a ray fallingonthe surface fromair,
suffersadeviationof 150
whenthe angle of incidence is400
.
Findn by Snell’slawandthenfindc=41.140
17 Two thin lenses when in contact produce a net power of +10D. If they are at 0.25m
apart, the net power falls to +6 D. Find the focal lengths of the two lenses
Ans. 0.125m, 0.5m)

18
A glassprismhas an angle of minimumdeviationD in air. What happens to the value of
D if the prism is immersed in water? Ans.
Decreases
19 Draw a ray diagram forthe patfollowedbythe rayof lightpassingthrougha glass prism
immersed in a liquid with refractive index greater than glass.
Three rays of light red (R) green (G) and blue (B) are incident on the surface of a right
angledprismasshowninfigure.The refractive indices for the material of the prism for
red green and blue are 1.39, 1.43 and 1.47 respectively. Trace the path of the rays
throughthe prism.How will the situationchange if the rayswere fallingnormallyonone
of the faces of an equilateral prism?
(Hint Calculate the critical angle for each and if the angle of incidence on the surface
AC is greater, then TIR will take place.)
20 Showthat the angle of deviationforasmall angled prism is directly proportional to the
refractive index of the material of the prism. One of the glass Prisms used in Fresnel’s
biprismexperimenthasrefractive index1.5.Findthe angle of minimum deviation if the
angle of the prism is 30
. (3)
(D= (n-1) A, 1.50
)
21 . In the given diagram, a ray of light undergoes total internal reflection at the point C
whichison the interface of two different media A and B with refractive indices1.7 and
1.5 respectively. Whatisthe minimumvalue of angle of incidence? Can you expect the
ray of light to undergo total internal reflection when it falls at C at the same angle of
incidence while entering from B to A. Justify your answer?
Ans.Use 0
0.88 C=61.7r
d
n
SinC and
n
  so i=61.80
nofor TIR ray of lightmusttravel
from denser to rarer from B to A)
22 The velocity of light in flint glass for wavelengths 400nm and 700nm are 1.80x108
m/s
and 1.86x108
m/s respectively. Find the minimum angle of deviation of an equilateral
prism made of flint glass for the given wavelengths.
(For 400nm D=520
and for 700nm D=480
)
n1=1.7
n2=1.5
C
A
B

OPTICAL INSTRUMENTS
GIST
1  Human eye:
 Eye lens: crystalline
 Cilliary muscles: lens is held in position by these.
 Iris: Circular contractible diaphragm with an aperture near the centre.
 Pupil: the circular aperture is pupil. It adjusts controlling light entering the eye.
 Power of accommodation: ability of pupil for adjusting focal length.
 Far point: the maximum distant point that an eye can see clearly.
 Near point: closest distant that eye lens can focus on the retina.
 Range of vision: distant between near point and far point.
2  Defects of vision:
Myopia: image formed in front of the retina. Correction-using concave lens.
Hypermetropia- image behind the retina. Correction-using convex lens.
Presbiopia-low power of accommodation. Correction-bifocal lens.
23 In the givendiagrama pointobjectiskeptat the Focus F of the convex lens. The ray of
light from the lens falls on the surfaces AB and BC of a right angled glass prism of
refractive index 1.5 at an angle 420
.Where will be the final image formed? Draw a ray
diagramto showthe positionof the final image formed. What change do you expect in
your answer if the prism is replaced by a plane mirror?
C=41.80
Ans- at F itself, no change
F
A
B
C

Astigmatism-corneahas differentcurvature indifferentdirection.Correction-usingcylindrical Lens.
3
4

5 Astronomical Telescope: (Image formed at infinity –
Normal Adjustment)
I
Image at
infinity
•
Fe
α
α
Fo
Objective
Eyepiece
fo fe
Po Pe
Eye
β
fo + fe = L
Focal length of the objective is much greater than that of the eyepiece.
Aperture of the objective is also large to allow more light to pass through it.
6 Angular magnification or Magnifying power of a telescope in normal adjustment
7 Newtonian Telescope: (Reflecting Type)
Concave Mirror
Plane Mirror
Eyepiece
Eye
Light
from star
M =
fo
fe
Magnifying Power:
8 Cassegrain telescope refer from NCERT / refer Page no 83

QUESTIONS
MICROSCOPE AND TELESCOPE
*1. You are givenfollowingthree lenses. Which two lenses will you use as an eyepiece and as
an objective to construct an astronomical telescope?
Lens Power(P) Aperture (A)
L1 3D 8 cm
L2 6D 1 cm
L3 10D 1 cm
Ans- The objective of anastronomical telescope shouldhave the maximumdiameterandits
eyepiece should have maximum power. Hence, L1 could be used as an objective and L3
could be used as eyepiece.
2
2. Draw a ray diagram of a reflecting type telescope. State two advantages of this telescope
over a refracting telescope.
2
3. Draw a ray diagram of an astronomical telescope in the normal adjustment position, state
two drawbacks of this type of telescope.
2
4. Draw a ray diagram of a compound microscope. Write the expression for its magnifying
power.
2
5. The magnifying power of an astronomical telescope in the normal adjustment position is
100. The distance between the objective and the eyepiece is 101 cm. Calculate the focal
lengths of the objective and of the eye-piece.
2
6. How doesthe ‘resolvingpower’of anastronomical telescope get affected on (i) Increasing
the aperture of the objective lens? (ii) Increasing the wavelength of the light used?
2
7. What are the two ways of adjusting the position of the eyepiece while observing the
Final image in a compound microscope? Which of these is usually preferred and why?
Obtainan expressionforthe magnifying power of a compound microscope. Hence explain
why(i) we preferboththe ‘objective’andthe ‘eye-piece’ tohave small focal length? and (ii)
we regardthe ‘length’of the microscope tube tobe nearlyequal to be separation between
the focal pointsof itsobjective anditseye-piece? Calculate the magnificationobtained by a
compound microscope having an objective of focal length 1.5cm and an eyepiece of focal
length 2.5 cm and a tube length of 30.
5
8. What are the two main considerations that have to be kept in mind while designing the
‘objective’ of an astronomical telescope?
Obtain an expression for the angular magnifying power and the length of the tube of an
astronomical telescope in its ‘normal adjustment’ position.
An astronomical telescope havingan ‘objective’ of focal length 2m and an eyepiece of focal
length1cm isusedto observe apairof starswithan actual angularseparation of 0.75. What
would be their observed angular separation as seen through the telescope?
5

Hint- observed angular separation = 0.75’ ×200 = 150’
*9. Cassegraintelescope uses two mirrors as shown inFig. Sucha telescope is built withthe
mirrors20 mm apart. If theradius of curvature of thelarge mirroris 220 mmand the small
mirror is 140mm,where willthe final image of anobjectat infinitybe? Thefollowingfigure
shows a Cassegraintelescope consistingof a concavemirrorand a convexmirror.
Distance betweenthe objective mirrorand thesecondary mirror,d = 20 mm
Radiusof curvatureof the objectivemirror,R1=220 mm
Hence,focallength of the objectivemirror,
Radiusof curvatureof the secondarymirror,R1=140 mm
Hence,focallength of the secondary mirror,
Theimage of an objectplacedatinfinity,formedbytheobjectivemirror, will actas a virtual
object for thesecondary mirror.
Hence,the virtualobjectdistancefor the secondarymirror,
Applyingthe mirrorformulafor the secondarymirror,we can calculate image distance(v)as:
Hence,the final imagewill be formed315 mmawayfrom thesecondary mirror.Light incident
normallyon a planemirror attachedto agalvanometer coil retraces backwardsas shown in
*10. Thebest positionof the eyefor viewing througha compoundmicroscopeis at theeye-
ringattached tothe eyepiece.The precise location of the eyedepends on the separation
betweentheobjective lensandthe eyepiece.Anangularmagnification(magnifying power)
of 30X is desiredusinganobjectiveof focallength1.25cmandan eyepiece of focal length
5 cm.How will you set up the compoundmicroscope?
Ans - Separation between theobjectivelens and theeyepiece
5

DEFECTS OF VISION
1. Amyopic person has beenusingspectacles of power −1.0 dioptre for distant vision.Duringold age
healsoneedstouse separate readingglassof power+2.0 dioptres.Explainwhatmayhave happened.
Ans -
Thepower of the spectaclesusedby the myopic person,P = −1.0 D
Focallengthof the spectacles,
Hence,the farpointof theperson is 100 cm. He might havea normalnear point of 25 cm.Whenhe uses
the spectacles, the objects placed atinfinity producevirtualimages at 100 cm.He uses the abilityof
accommodation of theeye-lensto see theobjects placedbetween 100 cmand 25 cm.
During oldage, theperson uses reading glasses of (power, P=100/50)
Theability of accommodationis lost in oldage.This defectis
calledpresbyopia.As a result, he is unable to seeclearly theobjects placedat 25 cm.
3
2. Answerthe followingquestions:
(a)Theanglesubtended atthe eyeby an object is equal to the anglesubtended attheeye by the
virtualimageproducedbyamagnifyingglass.Inwhatsensethendoesamagnifyingglassprovideangular
magnification?
(b)Inviewingthroughamagnifyingglass,one usuallypositionsone’s eyes veryclose to the lens. Does
angularmagnification changeif theeye is movedback?
(c)Magnifyingpowerof asimple microscopeisinverselyproportionaltothefocal lengthof the lens.What
thenstops us from using aconvex lens of smallerand smaller focallengthand achieving greater
andgreatermagnifyingpower?
(d)Whymust both theobjectiveand the eyepieceof a compoundmicroscopehave short focal
lengths?
(e)When viewingthrough a compound microscope, our eyes should bepositioned noton the
eyepiecebut a short distanceawayfrom itfor best viewing.Why?How muchshouldbe thatshort
distance between theeye and eyepiece?
Ans -
(a)Thoughthe image sizeisbiggerthan theobject,the angular sizeof the image is equal tothe angular
sizeof the object.Amagnifying glass helps oneseethe objects placed closerthan theleast distance of
distinctvision (i.e.,25 cm).Acloser object causes alarger angular size.Amagnifying glass provides
angular magnification.Withoutmagnification, theobject cannotbe placed closerto theeye.With
magnification,the object canbe placed muchcloser tothe eye.
(b)Yes,the angularmagnificationchanges.Whenthe distance betweenthe eyeand a magnifying glass
is increased, theangularmagnification decreases a little.This is becausethe angle subtended atthe
eyeis slightlyless than the anglesubtended at the lens. Imagedistancedoes not have any effect on
angular magnification.
(c)The focal lengthof a convexlens cannotbe decreased by a greater amount.Thisis because making
lenseshavingverysmallfocallengthsisnoteasy.Spherical andchromaticaberrationsare producedbya
convexlens having avery smallfocallength.
(d) Theangularmagnification producedby the eyepieceof a compoundmicroscopeis
Where,
fe=Focal lengthof theeyepiece
Itcan be inferred that iffeis small,then angular magnificationof the eyepiecewill belarge.
5

Theangularmagnification of theobjective lens of a compoundmicroscopeis given as
Where,
=Object distance for theobjectivelens
=Focal lengthof theobjective
In thecase of amicroscope,the objectiskeptclosetothe objectivelens.Hence,the objectdistanceisvery
little.Since issmall, willbe evensmaller.Therefore, and arebothsmallin the given condition.
(e)Whenwe place oureyes tooclose tothe eyepieceof acompoundmicroscope,we are unabletocollect
muchrefractedlight.Asaresult,thefieldof view decreases substantially.Hence,theclarity of theimage
gets blurred.
3. Amanwith normal nearpoint (25 cm)reads a book withsmallprint using amagnifyingglass: a
thinconvex lens of focallength 5 cm.
(a) What is theclosestandthe farthestdistanceatwhichhe shouldkeepthelensfromthe pageso that
he canread the book when viewingthrough the magnifyingglass?
(b)Whatisthemaximumandtheminimumangularmagnification(magnifyingpower) possible using
theabove simple microscope?
Ans -
(a)Focallengthof the magnifyingglass,f = 5 cm
Least distance of distance vision,d = 25 cm
Closesto objectdistance= u
Image distance, v= −d = −25 cm
Accordingto thelens formula,we have:
Hence,the closestdistanceat whichthe person canread thebook is 4.167 cm. For theobjectat
thefarthestdistant(u’), the imagedistance According to the lens formula,we have:
Hence,the farthest distance atwhich theperson can readthe book is 5cm.
(b)Maximum angular magnification is given by therelation:
5

CONCEPT MAP
Optical Instruments

Wave Optics
GIST

INTERFERENCEOF WAVES

DIFFRACTION OF LIGHT AT A SINGLE SLIT ;
Width of Central Maximum:
O
0
1
2
3
4
5
6
7
8
9
10
11
12
P1
N
A
B λ
θ1
θ1
θ1
λ/2
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Slit
Screen
Plane
Wavefront
Bright
Dark
D
d
y1
y1 = D λ / d
Since the Central Maximum is
spread on either side of O, the
width is
β0 = 2D λ / d

POLARISATION OF LIGHT WAVES :
Malus’ Law:
When a beam of plane polarised light is incident on an analyser, the intensity I of light transmitted
from the analyser varies directly as the square of the cosine of the angle θ between the planes of
transmission of analyser and polariser.
Polarisation by Reflection and Brewster’s Law:
(2)

CONCEPT MAP
WAVE NATURE OF LIGHT

QUESTIONS
Huygen'sPrinciple
1. Draw a diagram to show the refraction of a plane wave front incident on a convex lens and
hence draw the refracted wave front.
1
2. What type of wavefront will emerge from a (i) point source, and (ii) distance light source? 1
3. Define the term wave front? Using Huygen’s construction draw a figure showing the
propagationof a plane wave reflectingatthe interface of the twomedia. Show that the angle
of incidence is equal to the angle of reflection.
3
4. Define the term ‘wavefront’. Draw the wavefront and corresponding rays in the case of a (i)
divergingspherical wave (ii) planewave.Using Huygen’s construction of a wavefront, explain
the refraction of a plane wavefront at a plane surface and hence deduce Snell’s law.
3
Interference
1. How doesthe angularseparationof interference fringeschange,inYoung’sexperiment,when
the distance between the slits is increased?
Ans-when separation between slits (d) is increased, fringe width β decreases.
1
2. How the angularseparationof interference fringes in young would’s double slit experiment
change when the distance of separation between the slits and the screen is doubled?
Ans-No effect (or the angular separation remains the same)
1
*3. Indouble-slitexperiment using light of wavelength 600 nm,the angular width of afringe
formedon adistant screenis 0.1º.Whatis the spacingbetweenthe two slits?
Ans- Thespacing between theslits is
2
*4. If the pathdifference produceddue tointerferenceof lightcomingoutof twoslitsforyellow
colourof lightat a pointonthe screenbe 3λ/2, whatwill be the colourof the fringe atthat
point?Give reasons.
Ans.The givenpathdifference satisfiesthe conditionforthe minimumof intensityforyellow
light,Hence whenyellowlightisused,adark fringe will be formedatthe givenpoint.If white
lightisused,all componentsof white lightexceptthe yellow one wouldbe presentatthat
point.
2
5. State two conditions to obtain sustained interference of light. In Young’s double slit
experiment,usinglightof wavelength400 nm, interference fringes of width ‘X’ are obtained.
The wavelengthof lightisincreasedto600 nm and the separationbetweenthe slitsis halved.
In orderto maintain same fringe with, by what distance the screen is to be moved? Find the
ration of the distance of the screen in the above two cases.
Ans-Ratio-3:1
3
6. Two narrow slits are illuminated by a single monochromatic source. Name the pattern
obtainedonthe screen.One of the slits is now completely covered. What is the name of the
patternnowobtainedon the screen? Draw intensity pattern obtained in the two cases. Also
write two differences between the patterns obtained in the above two cases.
3
*7. In Young’s double-slit experiment a monochromatic light of wavelength λ, is used. The
intensity of light at a point on the screen where path difference is λ is estimated as K units.
What is the intensity of light at a point where path difference is λ /3?
Ans-K/4
3
*8. Abeamof lightconsistingof twowavelengths,650nmand 520 nm, is used
toobtaininterferencefringesinaYoung’sdouble-slitexperiment.(a)Findthedistance of thethird
brightfringeonthe screenfromthe centralmaximumforwavelength650nm.(b)Whatis
theleastdistancefromthecentralmaximumwherethe brightfringesdue toboththe
wavelengthscoincide?
Ans-a)
3

b)
*9. Inadouble-slitexperimentthe angularwidthof afringe isfoundtobe0.2°on a screen placed 1
m away.The wavelengthof lightusedis600 nm.What willbe theangularwidthofthe fringeif
the entire experimentalapparatusisimmersedin water?Take refractiveindex of waterto be
4/3.
Ans-
3
*10 A narrowmonochromaticbeamof lightof intensityIisincidentaglassplate.Another
identical glassplate iskeptclose tothe firstone andparallel toit.Each plate reflects25% of
the incidentlightandtransmitsthe reaming.Calculatethe ratioof minimumandmaximum
intensityinthe interference patternformedbythe twobeamsobtainedafterreflectionfrom
each plate.
Ans.Let I be the intensityof beamIincidentonfirstglassplate.Eachplate reflects25% of
lightincidentonitandtransmits75%.
Therefore,
I1 =I; andI2 = 25/100I = I/4;I3 =75/100 I = 3/4I;I4 = 25/100 I3 = 1⁄4 x 3⁄4 I = 3/16 I
I5= 7/100 I4= 3⁄4 x 3/16 I = 9/64 I
Amplitude ratioof beams2and 5 isR = √ I2/I5 = √I/4 x 64/91 = 4/3
Imin/Imax = [r-1/r+1]2 = [4/3-1 / 4/3+1]2 = 1/49 = 1:49
3
*11 In a two slitexperimentwithmonochromaticlight,fringesare obtainedonascreenplacedat
some distance Dfrom the slits.If the screenismoved5 x 10-2
m towardsthe slits,the charge
infringe widthis3 x 10 -5
m. If the distance betweenthe slitis10-3
m. Calculate the
wavelengthof the lightused.
Ans.The fringe widthinthe twocases will be β= Dλ/d;β‘= D’λ/d
β - β’ = (D-D’)λ/d;orwavelengthλ=(β - β’ )d/ (D-D’) ButD-D’ = 5 x 10-2
m
β - β’ = 3 x 10-5
m , d= 10-3
m;λ = 3 x 10-5
x 10-3
/5 x 10-2
= 6 x 10-7
m= 6000A
12. Two Sourcesof IntensityIand4I are usedin an interference experiment.Findthe intensityat
pointswhere the wavesfromtwosourcessuperimpose withaphase difference (i)zero(ii) π/2
(iii) π.
Ans-The resultantintensityata pointwhere phase difference isΦis I R = I1 +I2+2√I1I2 Cos Φ
As I1 =I and I2 = 4I therefore I R = I +4I+2√1.4I Cos Φ = 5I +4I cos Φ
(i) whenΦ =0 , I R = 5I +4I cos 0 = 9 I;(ii) whenΦ=π/2 , I R = 5I +4I cos π/2 = 5 I
(iii) whenΦ=π , I R = 5I +4I cos π = I
13. What are coherent sources of light? Two slits in Young’s double slit experiment are 5

illuminatedbytwodifferentsodiumlamps emitting light of the same wavelength. Why is no
interference pattern observed?
(b) Obtain the condition for getting dark and bright fringes in Young’s experiment. Hence
write the expression for the fringe width.
(c) If S isthe size of the source and itsdistance fromthe plane of the two slits,what should be
the criterion for the interference fringes to be seen?
Ans-c)
14. What are coherent sources? Why are coherent sources required to produce interference of
light? Give an example of interference of light in everyday life. In Young’s double slit
experiment, the two slits are 0.03 cm apart and the screen is placed at a distance of 1.5 m
away fromthe slits.The distance betweenthe central bright fringe and fourth bright fringe is
1 cm. Calculate the wavelength of light used.
Ans-(Numerical part)
5
15. What is interference of light? Write two essential conditions for sustained interference
patternto be producedon the screen. Draw a graph showingthe variationof intensityversus
the positiononthe screen in Young’s experiment when (a) both the slits are opened and (b)
one of the slitisclosed. What is the effect on the interference pattern in Young’s double slit
experimentwhen: (i) Screenismovedclosertothe plane of slits?(ii)Separationbetween two
slits is increased. Explain your answer in each case.
5
Diffraction
*1. Why a coloured spectrumisseen, when we look through a muslin cloth and not in other clothes?
Ans.Muslinclothismade of veryfine threadsandas such fine slitsare formed.White lightpassing
throughthese siltsgetsdiffractedgivingrise tocoloredspectrum.The central maximumiswhite
while the secondarymaximaare coloured.Thisisbecause the positionsof secondarymaxima
(exceptcentral maximum) dependonthe wavelengthof light.Inacoarse cloth,the slitsformed
betweenthe threadsare widerandthe diffractionisnotsopronounced.Hence nosuchspectrum
isseen.
2
2. A parallel beam of light of wavelength 600 nm is incident normally on a slit of width ‘a’. If the
distance between the slits and the screen is 0.8 m and the distance of 2nd order maximum from
the centre of the screen is 15 mm, calculate the width of the slit.
Ans-Difference betweeninterference and diffraction: Interference is due to superposition of two
distinct waves coming from two coherent sources. Diffraction is due to superposition of the
secondary wavelets generated from different parts of the same wavefront.
Numerical: Here, λ = 600 nm = 600 × 10−19 = 6 × 10−7 m
D = 0.8 m, x = 15 mm = 1.5 × 10−3 m,n = 2, a = ?
2
3. Answerthe followingquestions:
(a) Howdoesthe size and intensity of the central maximachangeswhenthe widthof the slit
isdouble ina single slitdiffractionexperiment?
(b)Inwhatwayisdiffractionfromeachslitrelatedtotheinterferencepatterninadouble-slit
experiment?
(c)Whenatinycircularobstacleisplacedinthepathof lightfromadistantsource,abrightspotis
2

seenat thecentreof the shadow of the obstacle.Explainwhy?
(d)Twostudentsareseparatedbya7 m partitionwallinaroom10 mhigh.If both lightandsound
wavescanbendaroundobstacles,how isitthat thestudentsare unable tosee eachothereven
thoughtheycanconverse easily?
Ans-
(a)Inasingle slitdiffractionexperiment,ifthewidthof theslitismade doubletheoriginalwidth,
thenthe sizeof thecentraldiffractionbandreducestohalfandtheintensityofthecentraldiffraction
bandincreasesuptofourtimes.
(b)Theinterferencepatterninadouble-slitexperimentismodulatedbydiffractionfromeachslit.
Thepatternistheresultof theinterferenceof the diffractedwavefromeachslit.
(c)Whenatinycircularobstacleisplacedin thepathof lightfromadistantsource,abrightspotis
seenat thecentreof the shadow of the obstacle.Thisisbecauselightwavesarediffractedfrom
the edgeof the circularobstacle,whichinterferesconstructivelyatthecentre of theshadow.This
constructiveinterferenceproducesabrightspot.
(d)Bendingof wavesbyobstaclesbyalarge angle ispossible whenthesize of the obstacle is
comparabletothewavelengthof thewaves.
Ontheone hand,thewavelengthofthe lightwavesistoosmall incomparisontothe sizeof the
obstacle.Thus,thediffractionanglewillbeverysmall.Hence,the studentsareunabletosee each
other.On theotherhand,thesizeof the walliscomparabletothe wavelengthof thesound
waves.Thus,thebendingof the wavestakesplace ata largeangle.Hence,thestudentsareable
toheareach other.
4. Why lightwaysdonot diffractedaroundbuildings,while radiowavesdiffracteasily?
Ans- For diffractiontotake place the wave lengthshouldbe of the orderof the size of the obstacle.
The radio waves (particularlyshortradiowaves)have wave lengthof the orderof the size of the
buildingandotherobstaclescomingintheirwayandhence theyeasilygetdiffracted.Since
wavelengthof the lightwavesisverysmall,theyare notdiffractedbythe buildings.
2
5. Draw the diagramshowingintensitydistributionof lightonthe screenfordiffractionof lightata
single slit.Howisthe widthof central maximaaffectedonincreasingthe (i) Wavelengthof light
used(ii) widthof the slit?Whathappensto the widthof the central maximaif the whole apparatus
isimmersedinwaterandwhy?
3
6. State the condition under which the phenomenon of diffraction of light takes place. Derive an
expression for the width of central maximum due to diffraction of light at a single slit. A slit of
width ‘a’ is illuminated by a monochromatic light of wavelength 700 nm at normal incidence.
Calculate the value of ‘a’ for position of
* (i) first minimum at an angle of diffraction of 30°
(ii) first maximum at an angle of diffraction of 30°
Ans-i)
ii)
5
Polarisation
1. At what angle of incidence should a light beam strike a glass slab of refractive index √3, such
that the reflected and the refracted rays are perpendicular to each other?
Ans-i=600
1
*2. What doesthe statement,“natural lightemittedfromthe sunis unpolarised” mean in terms of
the direction of electric vector? Explain briefly how plane polarized light can be produced by
reflection at the interface separating the two media.
Ans-The statement“natural light emitted from the sun is unpolarised” means that the natural
lightcomingfromsunis a mixture of waves,eachhavingits electric vectors directed in random
direction. When light falls on the interface separating two media, electrons start oscillating,
2

which produces reflected ray in addition to refracted ray. As light is a transverse wave,
therefore,oscillationinthe transverse direction will produce a light wave. Parallel oscillations
will not contribute to the light wave. When a light ray strikes an interface, the component of
electricvector, which is parallel to the interface, gets reflected. Therefore, the reflected light
wave is plane polarised light.
3. What isan unpolarizedlight?Explainwiththe help of suitable ray diagram how an unpolarized
light can be polarized by reflection from a transparent medium. Write the expression for
Brewster angle in terms of the refractive index of denser medium.
3
4. The critical angle betweenagiventransparentmediumandairisdenotedbyic, A ray of lightin
air mediumentersthistransparentmediumatanangle of incidence equal tothe polarizing
angle(ip).Deduce arelationforthe angle of refraction(rp) intermsof ic.
3
5 What is meant by ‘polarization’ of a wave? How does this phenomenon help us to decide
whether a given wave is transverse or longitudinal in nature?
5
QUESTIONS (HOTS)
VERY SHORT ANSWER QUESTIONS (1 MARK)
1. Air bubble is formed inside water. Does it act as converging lens or a diverging lens? 1
Ans: [Diverginglens]
2. A watertank is4 meterdeep.A candle flame iskept6meterabove the level.µforwater is 4 3 .
Where will the image of the candle be formed?. Ans : [6m below the water level] 1
SHORTANSWER QUESTIONS (2 MARKS)
1. Water is poured into a concave mirror of radius of curvature ‘R’ up to a height h as shown in
figure 1. What should be the value of x so that the image of object ‘O’ is formed on itself? 2
Fig 1 Fig 2
2. A pointsource S isplacedmidway between two concave mirrors having equal focal length f as
shown in Figure 2. Find the value of d for which only one image is formed. 2
3. A thindouble convex lensof focal length f is broken into two equals halves at the axis. The two
halvesare combinedasshowninfigure.Whatis the focal length of combination in (ii) and (iii).
2

4. How much water should be filled in a container 21cm in height, so that it appears half filled
when viewed from the top of the container  4 3a

  ? 2
5. A ray PQ incidentonthe refractingface BA is refracted in the prism BAC as shown in figure and
emergesfromthe otherrefractingface ACas RS such that AQ= AR.If the angle, of prism A= 60
and µ of material of prism is 3 then find angle  . 2
Hint : This a case of min .deviation 60  
SHORT ANSWER QUESTIONS (3 MARKS)
1. A convergingbeamof lightisinterceptedbyaslabof thickness t and refractive indexµ.By what
distance will the convergence point be shifted? Illustrate the answer. 3
2. In double slit experiment SS2 is greater than SS1 by 0.25 . calculate the path difference
betweentwointerferingbeamfromS1 andS2 for maximaonthe pointP as shown in Figure. 3
1
1X t

 
  
 

7. DUAL NATURE OF MATTER & RADIATION
GIST
ELECTRONEMISSION
1. There are three typesof electronemission,namely,ThermionicEmission,PhotoelectricEmission
and Field Emission.
2. The minimum energy required by an electron to escape from the metal surface is called work
function.
3. Work function is conveniently expressed in electron volts ( e V )
4. One electron volt is the energy gained or lost by an electron while passing through a potential
difference of one volt.
PHOTOELECTRIC EFFECT
1. The minimum energy required by an electron to come out from metal surface is called the work
function of a metal.
2. Photo electric effect is the phenomenon of electrons by metals when illuminated by light of
suitable frequency
3. Photo electric current depends on
i) The intensity of incident light
ii) The potential difference applied between two electrodes
iii) The nature of the emitter material
EXPERIMENTAL STUDY OF PHOTOELECTRIC EFFECT
1. The minimum negative potential given to the anode plate for which the photo electric current
becomes zero is called stopping potential.
2. The stopping potential Vo depends on i) The frequency of incident light and ii) the nature of
emittermaterial.Foragivenfrequencyof incidentlight,the stoppingpotential is independent of its
intensity.
eVo =(1/2)m 2
max maxv K
2. Belowa certainfrequency(thresholdfrequency) γ0 ,characteristicsof the metal ,no photo
electricemissiontakesplace,nomatterhow large the intensitymaybe.
EINSTEINS PHOTOELECTRIC EQUATION:ENERGYQUANTUM OFRADIATION
1. Light is composed of discrete packets of energy called quanta or photons.
2. The energycarriedbyeach photonisE = hν,where ν is the frequency and momentum p= h/λ. The
energy of the photon depends on the frequency γ of the incident light and not on its intensity.
3. Photo electric emission from the metal surface occurs due to absorption of a photon by an
electron
4. Einstein’s photo electric equation: Kmax = hν – φ0 or eV0 = hν - φ0.
PARTICLE NATURE OFLIGHT:THE PHOTON
1. Radiation has dual nature: wave and particle. The wave nature is revealed in phenomenon like
interference,diffractionandpolarization.The particle nature isrevealed by the phenomenon photo
electric effect.

2. By symmetry,matteralsoshouldhave dual nature: wave and particle. The waves associated with
the moving material particle are called matter waves or De Broglie waves.
3. The De Broglie wave length(λ) associatedwiththe movingparticle isrelatedtoits moment p as: λ
=h/p = h/mv
4.An equation for the De Broglie wavelength of an electron accelerated through a potential V.
Consider an electron with mass ‘m’ and charge ‘e’ accelerated from rest through a potential V.
K = eV
K = 1/2mv2
= p2
/2m
P2
= 2mK
P = √2mK = √2meV
λ = h/√2meV
Substitutingnumerical valuesof h, mand e
λ = (1.227/√V) nm.
CONCEPT MAP

QUESTIONS
ELECTRON EMISSION, PHOTO ELECTRIC EFFECT
1* If the intensity of incident radiation in a photoelectric experiment is doubled what, happens to
kinetic energy of emitted photo electrons? 1
2∗ Calculate the frequencyassociatedwith photon of energy 3.3 x 10 -10
J? Ans: ν = 5 x 10 23
Hz. 1
3 What is the momentum of a photon of energy 1 MeV? 1
Energy E = 1 MeV = 1.6 x 10 -13
J, p = E/c= 5.33x 10-22
Kgm/s
4∗ What happens to the velocity of emitted electrons when the wave length of incident light is
decreased?
5 If the frequency of incident radiation in a photocell is increased, does it affect the stopping
potential? If so how? 1
6 On what factor does the energy carried by a quantum of light depend? 1
7∗ The threshold wave length for photoelectric emission from a given surface is 5200Ǻ. Will photo
electricemissiontakesplace,if anultravioletradiationof one wattpowerisincident on it? 1
8 Name the element with highest work function and also the element with lowest work function.
Highest work function – Platinum ( 5.65eV )
Lowest work function – Caesium ( 2.14eV ) 2
9∗ Calculate the work function of a metal in eV if its threshold wavelength is 6800Å.
Ans: Work function = hc / λ0 = 1.825eV. 2
10 Work function of aluminium is 4.2eV. If two photons each of energy 2.5eV are incident on its
surface, will the emission of electrons take place? 2
11 A source of lightisplacedat a distance of 50cm froma photocell andthe cut off potential is found
to be V0.If the distance betweenthe lightsource andthe cell ismade 20cm, what will be the new
cut off potential?
Ans: Stopping potential is still Vo. 2
EINSTEIN’S PHOTO ELECTRIC EQUATION :ENERGY QUANTUM OF RADIATION
12 Which of the two photons is more energetic: red light or violet light? 1
13 What will be the stopping potential when a photon of 25eV is incident of metal surface of work
function 6eV? Ans : 19 volt 1
14 Why is alkali metal surfaces better suited as photosensitive surfaces? 1
15 Blue lightcan ejectelectronsfromaphoto-sensitivesurface while orange light can not. Will violet
and red light eject electrons from the same surface? 1
16 Two metalsA & B have workfunctions4eV &10eV respectively.Inwhichcase the threshold wave
length is higher? 1
17* A radio transmitter at a frequency of 880 kHz and a power of 10kW. Find the number of photons
emitted per second. 2
Ans: n = energy emitted per second/energy of one photon = 1.716 x 1031
.
18 A parallel beam of light is incident normally on a plane surface absorbing 40% of the light and
reflectingthe rest.If the incident beam carries 10W of power, find the force exerted by it on the
surface. 2
Ans : 5.33 x 10-8
N
19* No photoelectronsare emittedfromasurface,if the radiationis above 5000 Ǻ. With an unknown
wavelength, the stopping potential is 3V. Find the wave length. 3
Ans : 2262Ǻ
20* Illuminating the surface of a certain metal alternately with light of wave lengths0.35μm and
0.54μm, itwas foundthat the correspondingmaximumvelocitiesof photoelectronshave a ratio 2.
Find the work function of that metal. 3

Ans: 5.64eV
21* A beam of light consists of four wavelengths 4000Ǻ, 4800Ǻ, 6000Ǻ & 7000Ǻ, each of intensity
1.5mW/m2
.The beamfallsnormallyonanarea 10-4
m2
of a cleanmetallicsurface of work function
1.9eV.Assuming no loss of kinetic energy, calculate the number of photoelectrons emitted per
second. 3
Ans :E1 = 3.1eV, E2 = 2.58eV, E3 = 2.06eV, E4 = 1.77eV
Only the first three wave lengths can emit photo electrons.
Number of photo electrons emitted per second = IA ( 1/E1+1/E2+1/E3 )
= 1.12 x 1012
.
( Hint – convert eV into joule before substitution )
22 In an experiment on photo electric emission , following observations were made;
( i ) wave length of incident light = 1.98 x 10-7
m
( ii ) stopping potential = 2.5 V.
Find ( a ) kinetic energy of photo electrons with maximum speed
( b ) work function & ( c ) threshold frequency 3
Ans; ( a ) Kmax = 2.5eV ( b ) work function = 3.76eV
( c ) threshold frequency = 9.1x 1014
Hz
WAVE NATURE OF MATTER
1 What is the de Broglie wavelength (in Å) associated with an electron accelerated through a
potential of 100 V? 1
Ans: λ = 1.227 A o
2 Matter wavesassociatedwithelectronscouldbe verifiedbycrystal diffractionexperiments.Why?
Ans:The wave lengthof the matterwaves associatedwithelectronshaswave lengthscomparable
to the spacing between the atomic planes of their crystals. 1
3 How do matter waves differ from light waves as regards to the velocity of the particle and the
wave? 1
Ans:In case of matterwaves,the wave velocity is different from the particle velocity. But in case
of light, particle velocity and wave velocity are same.
4 An electron and an alpha particle have same kinetic energy. Which of these particles has the
shortest de- Broglie wavelength? 1
Ans: Alpha particle
5 The de Broglie wavelengthof anelectronis1 A0
. Find the velocity of the electron. 1
Ans: 7.3 x 10 6
m/s
6* Find the ratio of wavelength of a 10 k eV photon to that of a 10 keV electron. 2
Ans: 10 ( Hint: λphoton = 1.24 A0
, λelectron = 0.1227 A0
)
7* A proton and an alpha particle are accelerated through the same potential difference. Find the
ratio of the wavelengths associated with the two. 2
Ans: (Hint λ = h/ √2meV), λp : λα = 2 √2 : 1
8 Why macroscopic objects in our daily life do not show wave like properties? OR
Why wave nature of particles is significant in the sub-atomic domain only? 2
Macroscopic objects in our daily life do not show wave like properties because the wave length
associated with them is very small and beyond the scope of any measurement.
In the sub- atomicworld,massesof the particlesare extremelysmall leadingtoa wave length that
is measurable.
9* Showthat Bohr's secondpostulate 'the electronrevolvesaroundthe nucleus only in certain fixed
orbits without radiating energy can be explained on the basis of de Broglie hypothesis of wave
nature of electron. 2
Ans. The de Broglie wavelength for electron in orbit mvr = nh/ 2π
Thisis Bohr's secondpostulate.Ascomplete de-Brogliewavelengthmaybe incertainfixed
orbits, non-radiating electrons can be only in certain fixed orbits.

10* The de-Broglie wavelengthassociatedwithanelectronacceleratedthrough a potential difference
V is . What will be the de-Broglie wavelength
when the accelerating p.d. is increased to 4V? 2
11 Determine the acceleratingpotentialrequiredforan electron to have a de-Broglie wavelength of
1 Å 2
Ans: V = 150.6 V
12 An electron, an alpha particle and a proton have the same kinetic energy, which one of these
particleshas (i) the shortest and (ii) the largest, de, Broglie wavelength? 2
Ans:
1
=
2 mk
h
mE
 
13 The two linesA andB showninthe graph plotthe de-Broglie wavelength λ as function of 1/ √V (V
is the accelerating potential) for two particles having the same charge. Which of the two
represents the particle of heavier mass?
3
Ans: Slope of the graph is h/√2me.
Slope of A is smaller, so A represents heavier particle.
14* Find the ratio of de-Broglie wavelength of molecules of Hydrogen and Helium which are at
temperatures 270
C and 1270
C respectively. 3
Ans: de- Broglie wavelength is given by λH2 /λ He = √(mHe THe/mHTH = √(8/3)
21
4
V
V
,
v
1
2
21
2
2
1 





 

8. ATOMS & NUCLEI
GIST
Thomson’smodel of atom- Everyatomconsists of fuels
charged sphere in which electrons are embedded like
seeds in water melon.
Its drawbacks:couldn’texplainlarge angle scattering
& the origin of spectral series.
Rutherford’smodel of atom- i) Every atom consists of a
tiny central core, called the atomic nucleus, in which
the entire positivecharge andalmostentire massof the
atom are concentrated.
ii) The size of nucleusisof the order of 10-15
m , which is
verysmall as comparedtothe size of the atom which is
of the order of 10-10
m.
iii)The atomicnucleusissurroundedby certain number
of electrons. As atom on the whole is electrically
neutral, the total negative charge of electrons
surrounding the nucleus is equal to total positive
charge on the nucleus.
iv)These electrons revolve around the nucleus in
variouscircularorbitsas do the planetsaroundthe aun.
The centripetal force required by electron for
revolution is provided by the electrostatic force of
attraction between the electrons and the nucleus.
Limitations: couldn’t explain the stability of the
nucleus & the emission of line spectra of fixed
frequencies.
Distance of closestapproachof the alphaparticle in the
α particle scattering experiment
r0=2kZe2
1/2mv2
Impact parameter of the alpha particle
b=kZe2
cotθ/2
1/2mv2
Bohr’s model of atom
Limitations-applicable onlyforhydrogenlikeatoms&
couldn’t explain the splitting of spectral lines. (not
consider electro static force among the electrons)
Orbit radius of the electron around the nucleus r=e2
/4πЄ0mv2
, v=2πke2
/ nh, r=n2
h2
mke2
Energy of the electron in the nth orbit of hydrogen
atom
En= -me4
/8Є0
2
n2
h2
= -13.6/n2
eV
E=-2.18*10-18
J / n2
• Angular momentum of electron in any orbit is L = mvr = nh/2π, n=1,2,3,…

integral multiple of h/2π
• Wave number ν 1/λ = R(1/n1
2
– 1/n2
2
)
R=1.097 * 10+7
m-1
Atomic Number (Z)
No of protons in a nucleus
Mass Number (A)
Number of neutrons
No. of nucleons(protons + neutrons) in a nucleus
A-Z
Nuclear radius
R=R0 A1/3
Nuclear density
Ρ= 3m/4πR0
3
Isotopes
Same Z & different A
Ex, 1
H2,1
H3,1
h1, & C12
,C14
,C16
Isobars
Same A & different Z
[ 18Ar40
,20Co40
] & (1H3
, 2H3
)
Isotones
Map defect m
Same no. of neutrons
Mass of neutrons – 1H3
, 2He4
Binding energy Eb
E= m x c2
( m= mass of reactants – mass of
products)
1 a.m.u.= 931.5 Mev
Radioactive decay law
dN/dt=-λN
-dW/dt= R= Activity unit Bq.
No: of nuclei remaining un-decayed at any
instant of time
N =N0e-λt
OR
N=N0( ½)n
, n = t/t1/2
Half life
t1/2=0.693
λ
Mean life τ= 1/λ
3 types of radiations
Alpha,beta,gamma

Nuclear fission
Splittingof aheavynucleusintolighterelements.This
process is made use of in Nuclear reactor & Atom
bomb
Nuclear Reactoris baseduponcontrollednuclear
chainreactionand has
1) Nuclearfuel
2) modulator
3) control rods
4) coolant
5) shielding
Nuclear fusion
Fusingof lighter nuclei to form a heavy nucleus.This
process takes place in Stars & Hydrogen bomb.
ControlledThermonuclearFusion
In a fusionreactor-
a) highparticle densityisrequired
b) highplasmatemperature of 109
K
c) a longconfinementtimeisrequired

CONCEPT MAP
Nuclear energy
uclearEnergy

QUESTIONS
ALPHA PARTICLE SCATTERING
1. What is the distance of closest approach when a 5Mev proton approaches a gold nucleus (Z=79) (1)
Ans r0=
4
1
2
2
F
Ze
= 2.3 * 10-14
m.
2. Which has greater ionizing power: alpha or beta particle? (1)
BOHR’S ATOMIC MODEL
1. In Bohr’stheoryof model of a Hydrogenatom, name the physical quantitywhichequalstoan integral
multiple of h/2∏? (1)
Ans: Angular momentum
2. What is the relationbetween‘n’& radius ‘r’ of the orbit of electron in a Hydrogen atom according to
Bohr’s theory? (1)
Ans: r α n2
3. What is Bohr’s quantization condition? (1)
*4. For an electroninthe secondorbitof hydrogen,whatisthe momentof linearmomentumas per the
Bohr’s model? (2)
Ans: L=2(h/2∏) =h/∏ (moment of linear momentum is angular momentum)
5. Calculate the ratioof energiesof photons produced due to transition of electron of hydrogen atoms
from 2nd
level to 1st
and highest level to second level. (3)
E2-1 = Rhc[ 1/n1
2
– 1/n2
] = ¾ Rhc
E∞ - E1 = Rhc(1/22
– 1/∞) = Rhc / 4
SPECTRAL SERIES
*1. What is the shortest wavelength present in the Paschen series of hydrogen spectrum? (2)
Ans: n1=3, n2=infinity, λ=9/R=8204Ǻ
2. Calculate the frequency of the photon which can excite an electron to -3.4 eV from -13.6 eV.
Ans: 2.5x1015
Hz (2)
3. The wavelengthof the firstmemberof Balmerseriesinthe hydrogenspectrumis6563Å.Calculate the
wavelengthof the firstmember of Lyman series in the same spectrum.
Ans: 1215.4Å (2)
4. The ground state energy of hydrogen atom is -13.6eV.What is the K.E & P.E of the electron in this
state? (2)
Ans: K.E=-E=13.6 eV, P.E=-2K.E=-27.2 eV
*5. Find the ratio of maximum wavelength of Lyman series in hydrogen spectrum to the maximum
wavelength in Paschen Series? (2)
Ans: 7:108
*6. The energylevelsof anatomare as shownbelow. a) Which of them will result in the transition of a
photonof wavelength275 nm? b) Whichtransitioncorrespondstothe emission of radiation maximum
wavelength?
(3)
0eV A
-2eV B C
-4.5eV
D
-10eV

Ans: E=hc/λ=4.5eV, transition B Eα1/λ, transition A
*7. The spectrum of a star in the visible & the ultraviolet region was observed and the wavelength of
some of the lines that could be identified were found to be 824Å,970Å,1120Å,2504Å,5173Å
&6100Å.Which of these lines cannot belong to hydrogen spectrum? (3)
Ans: 970Å
(3)
9. What is the energy possessed by an ē for n= ?
Ans E=0 (1)
10. Calculate the ratioof wavelengthof photonemitteddue totransitionof electronsof hydrogen atom
from
i) Second permitted level to first level
ii) Highest permitted level to second level (3)
11. The radius of inner most electron orbit of H2 atom is 5.3 x 10-11
m. What are radii for n=2, 3, 4? (3)
Ans: rn = n2
r1
COMPOSITION OF NUCLEUS
1. What is the relation between the radius of the atom & the mass number? (1)
Ans: size α A1/3
2. What is the ratio of the nuclear densities of two nuclei having mass numbers in the ratio 1:4?
Ans: 1:1 (1)
3. How many electrons, protons & neutrons are there in an element of atomic number (Z) 11& mass
number (A) 24? (1)
Hint: ne = np =11, nn = (A – Z) = 24 -11 = 13
4. Select the pairs of isotopes & isotones from the following: (2)
i. 13
C6 ii.14
N7 iii.30
P15iv. 31
P15
Ans: isotopes-iii &iv ,isotones-i& ii
5. By what factor must the mass number change for the nuclear radius to become twice? (2)
1
33 2 2or timeA
NUCLEAR FORCE & BINDING ENERGY.
1. What is the nuclear force? Mention any two important properties of it.
(2)
2. Obtain the binding energy of the nuclei 56
Fe26 &209
Bi83 in MeV from the following data:
mH=1.007825amu,mn=1.008665amu, m(56
Fe26)=55.934939amu, m(209
Bi 83)=208.980388amu,
1amu=931.5MeV
3. Which nucleus has the highest binding energy per nucleon? (3)
Ans: Fe →492.26MeV,8.79MeV/A Bi →1640.3MeV,7.85 MeV
Hence56
Fe26
4. From the given data, write the nuclear reaction for α decay of 238
92U and hence calculate the energy
released. .92
238U = 238.050794u 4
2He = 4.00260u 234
90Th = 234.04363u (3)
5Binding Energy of 8O16 &
17C35
one 127.35 Mev and 289.3 Mev respectively. Which of the two nuclei is
more stable stability & BE/N? (2)
RADIOACTIVITY
1. How is a  particle different from an electron? (1)
2. Draw graph between no. of nuclei un-decayed with time for a radioactive substance (1)
3. Amongthe alpha,beta& gamma radiations,which are the one affected by a magnetic field?(1)
Ans: alpha & beta
4. Why do α particleshave highionizingpower? (1)
Ans: because of their large mass & large nuclear cross section
5. Write the relationship between the half life & the average life of a radioactive substance. (1)

Ans: T =1.44t1/2
6. If 70% of a givenradioactivesample isleftun-decayedafter 20 days, what is the % of original sample
will get decayed in 60 days? (2)
7. How does the neutron to proton ratio affected during (i) decay ii) α decay (2)
8. A radioactive sample havingN nuclei hasactivityR.Write anexpressionforitshalf life in terms of R &
N. (2)
Ans: R=Nλ, t1/2=0.693/λ =0.693N/R
9. Tritiumhas a half life of 12.5 years against beta decay. What fraction of a sample of pure tritium will
remain un-decayed after 25 years? (2)
Ans: N0/4
10. What percentage of a givenmassof a radioactive substance will be left un-decayed after 5 half-life
periods? (2)
Ans: N/N0 =1/2n
=1/32 =3.125%
11. A radioactive nucleus ‘A’ decays as given below:
β γ
A A1 A2
If the mass number & atomic number of A1 are 180 & 73 respectively, find the mass number & atomic
number of A & A2 (2)
Ans: A—180 & 72, A2—176 & 71
12. Two nuclei P & Q have equal no: of atoms at t=0.Their half lives are 3 & 9 hours respectively.
Compare the rates of disintegration after 18 hours from the start. (2)
Ans: 3:16
*13. Two radioactive materials X1& X2 have decay constants 10λ & λ respectively. If initially they have
the same no: of nuclei, find the time after which the ratio of the nuclei of X1 to that of X2 will be 1/e?
Ans: N=N0e-λt
, t=1/9λ (3)
*14. One gram of radium is reduced by 2.1mg in 5 years by decay. Calculate the half-life of Uranium.
Ans: 1672 years (3)
*16. At a given instant there are 25% un-decayed radioactive nuclei in a sample. After 10 seconds the
number of un-decayed nuclei reduces to 12.5 %.calculate the i) mean life of the nuclei ii) the time in
which the number of the un-decayed nuclei will further reduce to 6.25 % of the reduced number.
Ans: t1/2=10s, λ=.0693/s, τ=1/λ=14.43s, N=1/16(N0/8) →t=4x10=40s (3)
17. Half lives of two substances A and B are 20 min and 40 min respectively. Initially the sample had
equal noof nuclei. Findthe ratioof the remaining no: of nuclei of A and B after 80 min.
Ans: 1:4 (3)
NUCLEAR REACTIONS
1. Why heavy water is often used in a nuclear reactor as a moderator? (1)
2. Why is neutronveryeffectiveasa bombarding particle in a nuclear reaction? (1)
Ans: Being neutral it won’t experience any electrostatic force of attraction or repulsion.
3. Why is the control rods made of cadmium? (1)
Ans: They have a very high affinity on neutrons.
4. Name the phenomenon by which the energy is produced in stars. (1)
Ans: Uncontrolled Nuclear fusion
5. Name the physical quantities that remain conserved in a nuclear reaction? (1)
6. What is neutron multiplication factor? For what value of this, a nuclear reactor is said to be critical?
Ans: K=1 (2)
7. 4 nuclei of an element fuse together to form a heavier nucleus .If the process is accompanied by
release of energy,whichof the two:the parentorthe daughternuclei wouldhave higherbindingenergy
per nucleon. Justify your answer. (2)
8. If 200MeV energyisreleasedinthe fission of single nucleus of 𝑈92
235
, how much fission must occur to
produce a power of 1 kW. (3)

9. ELECTRONIC DEVICES
GIST
ENERGY BAND DIAGRAMS
 In metals, the conduction band and valence band partly overlap each other and there is no
forbidden energy gap.
 In insulators, the conduction band is empty and valence band is completely filled and
forbidden gap is quite large = 6 eV. No electron from valence band can cross over to
conduction band at room temperature, even if electric field is applied. Hence there is no
conductivity of the insulators.
 In semiconductors, the conduction band is empty and valence band is totally filled. But
the forbidden gap between conduction band and valence band is quite small, which is
about 1 eV. No electron from valence band can cross over to conduction band. Therefore,
the semiconductor behaves as insulator. At room temperature, some electrons in the
valence band acquire thermal energy, greater than energy gap of 1 eV and jump over to
the conduction band where they are free to move under the influence of even a small
electric field. Due to which, the semiconductor acquires small conductivity at room
temperature
Metals Insulators Semiconductors
Differences
DistinctionbetweenIntrinsicandExtrinsicSemiconductor
Intrinsic Extrinsic
1 It ispure semiconductingmaterialand
no impurityatomsare addedto it
1 It ispreparedby dopinga small quantityof
impurityatomstothe pure semiconducting
material.
2 Examplesare crystalline formsof pure
siliconandgermanium.
2 Examplesare siliconandgermaniumcrystalswith
impurityatomsof arsenic,antimony,
phosphorousetc.orindium, boron,aluminumetc.
3 The numberof free electronin
conductionbandand the numberof
holesinvalence bandisexactlyequal
and verysmall indeed.
3 The numberof free electronsandholesisnever
equal.There isexcessof electronsinn-type
semiconductorsandexcessof holesinp-type
semiconductors.
4 Its electrical conductivityislow 4 Its electrical conductivityishigh.
5 Its electrical conductivityisafunction
of temperature alone.
5 Its electrical conductivitydependsuponthe
temperature aswell asonthe quantityof impurity
atomsdopedinthe structure.
Distinction between n-type and p-type semiconductors

n-type semiconductors p-type semiconductors
1 It isan extrinsicsemiconductors
whichisobtainedbydopingthe
impurityatomsof Vthgroup of
periodictable tothe pure germanium
or siliconsemiconductor.
1 It isan intrinsicsemiconductorswhichisobtained
by dopingthe impurityatomsof IIIgroupof
periodictable tothe pure germaniumorsilicon
semiconductor.
2 The impurityatomsadded,provide
extraelectronsinthe structure,and
are calleddonoratoms.
2 The impurityatomsadded,create vacanciesof
electrons(i.e.holes) inthe structure andare called
acceptor atoms.
3 The electronsare majoritycarriers
and holesare minoritycarriers.
3 The holesare majoritycarriersand electronsare
minoritycarriers.
4 The electrondensity(ne) ismuch
greaterthan the hole density(nh)i.e.
ne>>(nh)
4 The hole density(ne) ismuchgreaterthan the
electrondensity (nh)i.e.nh>>ne
5 The donor energylevelisclose tothe
conductionbandand far awayfrom
valence band.
5 The acceptor energylevel isclose tovalence band
and isfar away fromthe conductionband.
6 The Fermi energylevel liesinbetween
the donor energylevel and
conductionband.
6 The Fermi energylevel liesinbetweenthe
acceptor energylevel andvalence band.
P-njunctiondiode
Two importantprocessesoccurduringthe formationof p-njunctiondiffusionanddrift.
the motionof majoritycharge carriers give rise todiffusioncurrent.
Due to the space charge on n-side junctionandnegativespace charge regiononp-side the electricfield
isset upand potential barrierdevelopsatthe junctionDue toelectricfielde- onp-side movestonand
holesfromn-side top-side whichiscalleddriftcurrent.
In equilibriumstate,there isnocurrentacrossp-n junction andpotential barrieracrossp-njunctionhas
maximumvalue .
The widthof the depletionregionandmagnitude of barrierpotential dependsonthe nature of
semiconductoranddopingconcentrationontwosidesof p-njunction –
ForwardBias
P-njunctionisFB whenp-type connectedtothe +ve of batteryandn-type connectedto –ve battery
Potential barrierheightisreducedandwidthof depletionlayerdecreases.
Reverse Bias
P-njunctioninRB p-type connected tothe –ve batteryand n-type connectedto+ve
Resistance of p-njunctionishightothe flow of current.

0
Rectification

• There are twotypesof transistor – NPN & PNP
• Applicationsof transistor
(1) Transistoras a switch- (2) Transistoras an amplifier
• Transistoras an oscillator
Transistor- Switch
Whena transistoris usedincut off or saturatedstate,itbehavesasa switch.
Transistor-Amplifier_Anamplifierisa device whichis usedfor increasingthe amplitude of variation
of alternatingvoltage or current or power,thusit producesan enlargedversionofthe input signal.
For Circuit diagram referNcert diagram
LED PHOTODIODE SOLARCELL
Forward biased Reverse biased No external baising,Itgenerates
emf when solar radiation fallson
it.
Recombination of electrons and
holes take placeatthe junction
and emits e m radiations
Energy is supplied by lightto take
an electron from valenceband to
conduction band.
Generation of emf by solar cellsis
due to three basic process
generation of e-h pair,separation
and collection
It is used in Burglar alarm,remote
control
It is used in photo detectors in
communication
It is used in satellites,space
vechicles calculators.

Transistor-Oscillator-
• In an oscillator,we getacoutputwithoutanyexternal inputsignal.Inotherwords,the outputin
an oscillatorisself- sustained.OscillatorconvertsD.CintoA.C
Digital Electronics–Logic Gates
• The three basic LogicGates are
(1) OR Gate
OUTPUT Y= A + B
(2) ANDGate
OUTPUT Y=A.B
(3) NOT GATE
OUTPUT Y=Y’
COMBINATION OFGATES
__
(1) NORGATE--OUT PUT Y = A+B
__
(2) NANDGATE--OUT PUT Y= A .B

CONCEPT MAP
Semiconductor and electronic devices

QUESTIONS
SEMICONDUCTORS
1. What is the orderof energygapin an intrinsicsemiconductor? (1)
2. How doesthe energygapvary in a semiconductorwhendopedwithpenta -valentelement? (1)
3. How doesthe conductivitychange withtemperature insemiconductor? (1)
4. What type of semiconductorwe getwhen:Ge isdopedwithIndium?Si isdopedwithBismuth?(1)
5. In a semiconductorconcentrationof electronis8 x 1013
cm-3
andholes5 x 1012
cm-2
: isit P or
N type semiconductor? (1)
6. Draw energygap diagramof a P Type semiconductor? (1)
7. What is Fermi energylevel? (1)
8. Energy gap of a conductor,semiconductor,insulatorare E1, E2, E3 respectively.Arrange themin
increasingorder. (1)
9. Name the factor that determines the element as a conductor or semiconductor? (1)
10. Why semiconductorsare opaque tovisible lightbuttransparenttoinfraredradiations? (2)
Ans:The photonsof infraredradiationhave smaller energies, so they fall to excite the electrons in the
valence band.Hence infraredradiationspass throughthe semiconductors as such; i.e. a semiconductor
is transparent to infrared radiation
11. The ratio of numberof free electronstoholesne/nh for two different materials A and B are 1 and <1
respectively. Name the type of semiconductor to which A and B belongs. (2)
Ans:If ne/nh =1 . Hence A is intrinsicsemiconductor.If ne/nh<1, ne<nh hence Bis P-type.
12. Differentiate the electrical conductivity of both types of extrinsic semiconductors in terms of the
energy band picture. (2)
P-NJUNCTIONDIODE
1. How doesthe widthof depletionlayerchange,inreversebiasof a p-njunctiondiode? (1)
2. Draw VI characteristicgraphfor a Zenerdiode? (1)
3. In a givendiagram,is the diode reverse(or) forwardbiased? (1)
Ans:Reverse biased.
4. Why Photodiode usuallyoperatedatreverse bias? (2)
5. State the factor whichcontrolswave lengthandintensityof lightemittedbyLED. (2)
Ans:(i) Nature of semi-conductor
(ii) ForwardCurrent
6. With the helpof a diagram showthe biasingof lightemittingdiode.Give twoadvantagesover
conventional incandescentLamp. (2)
Ans:Mono chromatic,Consume lesspower.

8. Draw a circuitdiagramto show,howisa photodiode biased? (2)
9. Pure SI at 300K have equal electronandholesconcentration1.5x 1016
per m3
.Dopingby Indium
increaseshole concentrationto4.5 x 1022
per m3
.Calculate new electronconcentration.
Ans:nenh = ni
2
(2)
10. V-Icharacteristicsof SIdiode isgiven.Calculate diode resistance forbiasvoltage 2V. (2)
Ans:R = V / I = 2/70 x 10 3
Ohms
11. What isan ideal diode?Drawitsoutput wave form.
13. In the followingdiagram,identifythe diodeswhichare inforwardbiasedandwhichare inreversed
biased.
*14. A semiconductorhasequal electronandhole concentrationsof 6x108
/m3
.Ondopingwithacertain
impurity,the electronconcentrationincreasesto9x1012
/ m3
. (2)
(i) Identifythe new semiconductorobtainedafterdoping.
(ii) Calculate the newhole concentrations.
Ans:(i) n-type semiconductor.
(ii) nenh =ni
2
=> nh=6x108
x6x108
= 4x104
perm2
*15. Determine the currentthroughresistance “R”ineachcircuit.DiodesD1 and D2 are identical and
ideal.
2
+10V
Q.ii
-10V
R
0V
Q.iii
-5V
-12V
Q.iv
Q.i +5V
0V
+5V

Ans:In circuit(i) BothD1 and D2 are forwardbiasedhence bothwill conductcurrentandresistance of
each diode is“0”.Therefore I= 3/15 = 0.2 A
(iii) Diode D1 is forwardbiasand D2 is reverse bias,therefore resistanceof diode D1is“0”
and resistance of D2 isinfinite.Hence D1will conductandD2 do not conduct.No
currentflowsinthe circuit.
16. Fromthe givengraphidentifythe knee voltage andbreakdownvoltage. Explain? (2)
*17. Germaniumandsiliconjunctiondiodesare connectedinparallel.A resistance R,a 12 V battery,a
milli ammeter(mA) andKey(K) isclosed,acurrentbeganto flow inthe circuit.What will be the
maximumreadingof voltmeterconnectedacrossthe resistance R? (2)
Ans:The potential barrierof germaniumjunctiondiode is0.3vand siliconis0.7V,bothare forward
biased.Thereforeforconductionthe minimumpotential difference acrossjunctiondiodeis
0.3V.Max.readingof voltmeterconnectedacrossR=12-0.3=11.7V.
18.A Zenerdiode hasa contact potential of .8Vinthe absence of biasing.Itundergoesbreakdownforan
electricfieldof 10V/mat the depletionregionof p-njunction.If the widthof the depletionregionis
2.4µm?What shouldbe the reverse biasedpotentialforthe Zenerbreakdowntooccur? 2
*18. A germaniumdiode ispreferredtoasiliconone forrectifyingsmall voltages.Explainwhy? (2)
Ans: Because the energy gap for Ge (Eg = 0.7 ev) is smaller than the energy gap for Si (Eg = 1.1eV) or
barrier potential for Ge<Si.
19. On the basisof energybanddiagrams,distinguishbetweenmetals,insulatorsandsemiconductors.
(3)
SPECIAL DEVICES
*1. A photodiode isfabricatedfrom asemiconductorwithabandgap of 2.8eV.can itCan it detecta
wavelengthof 600nm?Justify? (2)
Ans:Energycorrespondingtowavelength600 nm is
E=hc/  = 6.6x10-34
x 3x108
joule =0.2eV.
600x10-9
It cannot detectbecause E<Eg

2. Which special type of diode actsas voltage regulator?Give the symbol. Draw itsV-Icharacteristics.
(3)
TRANSISTORS
1. How doesthe dc current gainof a transistorchange, whenthe widthof the base regionisincreased?
(1)
*2. Inonlyone of the circuitsgivenbelow,the lamp“L”glows.Identifythe circuit?Give reasonforyour
answer? (2)
Ans:In fig(i) emitter–base junctionhasnosource of emf.Therefore Ic=0, bulbwill notglow.Infig(ii)
emitter– base junctionisforwardbiased;therefore lamp“L”will glow.
(iii) emitter–base junctionisreceivedbiasedsothe bulbwill not glow.
*3. Whydo we preferNPN transistortoPNPfor fasteraction? (2)
Ans:For fasteractionNPN Transistorisused.In an NPN transistor,currentconductionismainlybyfree
electron,whereasinPNPtype transistor,itismainlyholes.Mobilityof electronsisgreaterthanthatof
holes.
4. In whichmode,the cut off,active orsaturation,the transistorisusedas a switch?Why? (2)
Ans:Cut off & saturation
5. In NPN transistorcircuit,the collectorcurrentis5mA. If 95% of the electronsemittedreachthe
collectorregion,whatisthe base current? (2)
Here,
Ic=95% of Ie = (95 / 100 ) Ie
Ie = (100 / 95) × 5 mA = 5.26mA,
Ie=Ic+ Ib
Ib = 0.25 mA
6. A studenthasto studythe inputandoutputcharacteristicsof a n-p-nsilicontransistorinthe common
emitterconfiguration.Whatkindof a circuitarrangementshouldshe use forthispurpose? Draw the
typical shape of inputcharacteristicslikelytobe obtainedbythatstudent.
(Ans:Fig14.29, pg 493 & 494 NCERT-Part-2physics
7. Which of inputand outputcircuitsof a transistorhasa higherresistance andwhy? (3)
Ans:The outputcircuitof a transistorhasa higherresistance. Hint:The ratioof resistance of output
circuit(r0) is 104
timesthatof inputcircuitie ro =104
ri;
*8. Inthe circuitdiagramgivenbelow,avoltmeterisconnectedacrossa lamp.What changeswouldoccur
at lamp“L” and voltmeter“V”,whenthe resistorRisreduced?Give reasonforyouranswer.(3)
Ans:In the givencircuit,emitter –base junctionof N-P-N transistor is forwardbiased.

When“R” decreases,IE increases.Because IC = IE – I B. Therefore IC will alsoincrease.Hence bulbwill
glowwithmore brightnessandvoltmeterreadingwill increase.
9. The base current of a transistor is 105 µA and collector current is 2.05 mA. (3)
a) Determine the value of  , Ie , and α
b) A change of 27 µA inthe base current producesa change of 0.65 mA in the collector current. Find
 a.c.
Ib = 105 × 10 -6
A Ic = 2.05 × 10 -3
A
 = Ic / Ib = 19.5
Also,
= 2.155 × 10 -3
Ie = Ib + Ic A
α = Ic / Ie = 0.95
Ib = 27µA = 27 × 10 -6
A
ac
= Ic / Ib = 24.1
10. Underwhat conditionsanamplifiercanbe convertedintoan oscillator?Draw a suitable diagram
of an oscillator. (3)
Hint: 1. when feedbackis positive. 2. Whenfeedbackfactorkis equal tol /Av.
11. Explainthroughalabeledcircuitdiagram, workingof atransistor,asan amplifierincommonemitter
configuration.Obtainthe expressionforcurrentgain, voltage gainandpowergain. (3)
12. Draw a circuitdiagram to studythe inputandoutputcharacteristicof an NPN transistorincommon
emitterconfiguration.Drawthe graphsforinputand outputcharacteristics. (3)
13. Define transconductance of a transistor. (2)
Ans:gm = ∆IC/∆VB
14. How doesthe collectorcurrentchange injunctiontransistorif the base regionhaslargerwidth?
Ans:Currentdecreases. (2)
15. The inputof commonemitteramplifieris2KΏ.Currentgainis 20. If the loadresistancesis
5KΏ. Calculate voltage gaintransconductance. (3)
Ans:gm = β / RI,Av = β RL/RI
16. Define input,outputresistance,currentamplificationfactor,voltage amplificationfactor,for
commonemitterconfigurationof transistor. (3)
17. A change 0.2 mA in base current,causesa change of 5mA incollectorcurrentina commonemitter
amplifier.

(i) FindA.Ccurrentgainof Transistor.
(ii) If inputresistance 2KΏandvoltage gainis75. Calculate loadresistance usedincircuit.
β AC currentgain= β ∆Ic / ∆ Ib (3)
19. In a transistorthe base currentis changedby20μa. This resultsina change of 0.02V inbase emitter
voltage anda change of 2ma incollectorcurrent. (3)
(i) Findinputresistance,
(ii) Transconductance.
20. Withthe helpof circuitdiagramexplainthe actionof atransistor. (3)
21. Draw the circuitdiagram tostudy the characteristicof N-P-N transistorincommonemitter
configuration.Sketchinput –outputcharacteristicforthe configuration.Explaincurrentgain,voltage
gain. (3)
22. Draw the transfercharacteristicsof a transistorincommonemitterconfiguration.Explainbrieflythe
meaningof the termactive regionandcut off regioninthischaracteristic. (3)
23. Explainwiththe helpof acircuitdiagram the workingof N-P-N transistorasa commonemitter
amplifier.Drawinputandoutputwave form. (3)
24. Draw a labeledcircuitdiagramof commonemitteramplifierusingP-N-Ptransistor.Define voltage
gainand write expression.Explainhowthe inputandoutputvoltage are outof phase 180o
for common
emittertransistoramplifier. (3)
25. The outputcharacteristicof transistoris shown.
(i) Findcurrentamplification
(ii) OutputResistance
Ic (mA)
Ib
0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 VCE (V)
LOGICGATES
*1. Moderntechnologyuse polysiliconinsteadof metal toformthe gate.Why? (1)
Ans:Polysiliconhashighconductivitycompared tometal.
2. Identifythe logicgate;Give itstruthtable andoutputwave form? (1)
10μA
20μA
30μA
40μA
50μA
60μA
10

Ans:NANDGATE.
*3. Draw the logiccircuitand the outputwave form forgivenoutputY=0, 0, 1, 1 (2)
Ans:The outputof the AND gate is Y = A.Bconsequentlythe inputof the ORgate are A and A.B . Then
the final Y = A + A.B
Inputfor ANDgate Output of Inputof output of
AND gate OR gate OR gate
A B Y= A.B A Y Y = A + Y
0 0 0 0 0 0
0 1 0 0 0 0
1 0 0 1 0 1
1 1 1 1 1
*4. Constructthe truth table forthe BooleanequationY=(A+B).Candrepresentbylogiccircuit. (2)
C
YA
B
Ans:The outputof OR gate isA+B. Consequently,the inputsof ANDgate are A+B & C Hence the Boolean
equationforthe givencircuitis Y=(A+B).C
*5. ConstructANDgate usingNANDGATE andgive itstruth table? (2)
Ans:ANDGate usingNANDGATE:-
A B Y= A.B

0 0 0
0 1 0
1 0 0
1 1 1
6. Identifywhichbasicgate OR,ANDand NOT isrepresentedbythe circuitsinthe dotted linesboxes1,2
and 3. Give the truth table forthe entire circuitforall possible valuesof A andB? (3)
Ans:The dottedline box 1representsaNOTgate. The dottedline box 2 representsanORgate.Here
we use de Morgan’stheorem.The dotted line 3representsANDgate.
7. Two inputwaveformsA andB showninfigure (a) and (b) are appliedtoan ANDgate.Write the
output (3)
Time 1 2 3 4 5 6
interval
InputA 0 1 1 0 0 1
InputB 0 0 1 1 0 0
Output 0 0 1 0 0 0
Y = A.B
Inputwaveform.
8. A circuitsymbol of a logicgate and twoinputwave formsA andB are shown.
a) Name the logic gate
b) Give the output wave form
A

B
a. Name the logicgate
b. Give the outputwave form (3)
Ans:Currentamplifier= ∆Ic / ∆ Ib = 9.5 – 2.5 / 50 x 10 -6
1. Identifythe Logicgate.
A
B
Y = A B
2. Draw the circuitof XOR gate.
AND
OR Y
AND
(3)
3. Identifythe Logicgate
OR
A
(A+B)
B
AND
A.B
NAND
A B Y
0 0 0
0 1 1
1 0 1
1 1 0

Ans:Y = (A+B) AB
4. Identifythe gate:
A A B
Y
B
Ans:ANDGate
5. A and b wave forminputgivenforNANDgate.Draw Output
10. COMMUNICATION SYSTEMS
GIST
1. COMMUNICATION
The sending and receiving of message from one place to another is called communication. Two
important forms of communication systems are (i) Analog and (ii) digital.
In analogcommunicationthe signal iscontinuous while in digital communication the signal is discrete.
2. THREE BASIC ELEMENTS OF COMMUNICATION
(i) Transmitter (ii) Communication channel (iii) Receiver
3. MODULATION
The superpositionof (audiofrequency)message signal (20Hz-20 kHz) over(highfrequency) carrierwave
(≈ 1MHz) is called modulation.
4. NEED FOR MODULATION:
* Size of antenna h= λ/4 so, for high frequency. Height will be large which is impossible.
* Effective power radiated by an antenna P α 2
1

* Mixing up of signals from different transmitters.
5. TYPES OF MODULATION
There are two broad types of modulation: (i) Continuous wave modulation
(ii) Pulse modulation.
1. Continuous wave modulation is of three types:
(i) Amplitude modulation (AM): In amplitude modulation, the amplitude of carrier wave varies in
accordance with instantaneous voltage of information (or message) signal.
(ii) Frequencymodulation(FM):Infrequencymodulation the frequency of carrier wave is varied in
accordance with instantaneous voltage of information signal.
(iii) Phase modulation(PM):Inphase modulation,the phase of carrier wave is varied in accordance
with the information signal.
6. Amplitude modulation

8. SPACE COMMUNICATION
Space communication uses free space between transmitter and receiver.
Space communication is via:
(i) ground waves (ii) space waves (iii) sky waves
9. GROUNDOR SURFACEWAVE PROPAGATION isa mode of wave propagation inwhichthe groundhas
a strong influence on the propagation of signal wave from the transmitting antenna to receiving
antenna.Inthispropagation,the signal wavesglidesoverthe surface of earth,Groundwavesare heavily
absorbed by earth and not suitable for long range communication. Ground wave propagation can be
sustained only at low frequencies (500 kHz-1500 kHz).
10. SKY WAVEPROPAGATION is a mode of wave propagationinwhichthe radiowave emitted from the
transmitterantennareachthe receivingantennaafterreflectionbyionosphere.Skywave propagationis
possible because of reflection of carrier signals from ionosphere or satellite.
11. SPACE WAVE PROPAGATION higher than 30MHz is that mode of wave propagation in which the
radiowaves emitted from the transmitter antenna reach the receiving antenna through space. These
radiowavesare calledspace waves.Itisalso called line of sight communication. Space wave is suitable
for UHF/VHF regions.
Band width of the signal
Type of signal Band width
Speech 2800 Hz
Music 20 KHz
Video 42 MHz
Video & Audio (T.V) 6.0 MHz
12. COVERING RANGE OF T.V. TRANSMITTING TOWER is d=√2Reh, where h is height of tower and Re
radius ofearth. T.V. waves are frequency modulated waves. VHF T.V. waves range from 47 to 230 MHz
and UHF T.V. waves have range from 470 to 960 MHz.
Maximum line of sight distance dm =√2RhT + √2RhR.
14. MAXIMUM USABLE FREQUENCY
It isthat highestfrequencyof radiowaveswhichwhensentatsome angle towardsthe ionosphere, gets
reflected from that and returns to the earth.
16. SATELLITE COMMUNICATION
The communicationsatellite isusedforreflectingskywaveswithoutanydisturbance.Its height is 35800
km above earth’s surface. To cover entire globe of earth simultaneously 3-satellites are employed.
II. IMPORTANT FORMULAE
1. Marconi antennaisgrounded,andits length= λ/4, where λis wavelengthof the wavestransmitted.It
is called quarter wave antenna.
2. Hertz antenna is not grounded, and its length = λ/2. It is called half wave antenna.

3. Side bandfrequenciesinAMwave are υSB = υc ± υmwhere υm isfrequencyof modulating(audio) signal.
4. Modulation index, ma = Em / Ec
Modulation index, ma= Emax – Emin / Emax + Emin
6. Coverage range (d) for a given height (h) of antenna
d = √2hR where R = radius of earth.
d = √2Rhr + √2RhR,where hT , hR are the heights of transmitter and receiver antennas.
7. Population covered = population density x area covered.
8. Number of channels,
N = Total band width of channels / Band width per channel
III. Communication System – Block Diagrams
1)
2)
3)
4)

5)
CONCEPT MAP
QUESTIONS
ELEMENTS OF COMMUNICATION SYSTEMS
1. Mention the functions of the transponder? (1)
Ans: A device fitted on the satellite which receives the signal and retransmits it after amplification.
2. What should be the length of dipole antenna for a carrier wave of 5 x 108
Hz? (1)
Ans: L = λ2 = cv x 2 = 3 x 108
/ 5 x 108
x 2 = 0.3m.
3. *A device X can convert one form of energy into another. Another device Y can be regarded as a
combination of a transmitter and a receiver. Name the devices X and Y. (1)
(a) Transducer (b) Repeater
4. Name the two basic modes of communication. Which of these modes is used for
telephonic communication? (2)
EM Waves and Communication

HINT:
Two basic modes of transmission are (i) Point-to-point and (ii) broad cast mode.
Point-to-point mode is used for Telephonic communication.
5. Differentiate an analog signal and a digital signal. How can an analog signal converted into a
digital signal?
6.
(2)
(2)
Hint: X= IF STAGE, Y = Amplifier
7.* Complete the following block diagram depicting the essential elements of a basic
communication system. (3)
ANS:TRANSMITTER,MEDIUMAND RECIEVER
8.Calculate the length of a half wave dipole antenna at (3)
(a) 1 MHz (b) 100 MHz (c) 1000MHz
What conclusion you draw from the results?
Hint: Length of dipole antenna, L = λ/ 2
(a) 150m (b) 1.5m (c) 15 cm
II. PROPAGATION OF EM WAVES
1. Name the types of communication that uses carrier waves having frequencies in the range
1012
to 1016
Hz.
Ans. Optical communication (1)
2. Write the expression for band width in FM. (1)
Ans. width = 2 times frequency of modulating signal
3. What is attenuation? (1)
4. What is the role of band pass filter in modulation circuit? (1)
Ans.If filters out low and high frequencies and only allow band of frequencies (wc – wm) to (wc+wm)
5. Distinguish between analog and digital communication. (1)
6. State the facts by which the range of transmission of signals by a TV tower can be increased?
Ans. by increasing height of transmitting antenna (1)
by increasing height of receiving antenna
7. What % of AMwave power is carried by side bands for m=1? (1)
8. Why moon cannot be used as a communicate satellite? (1)
9. Explain why medium waves are better parries of signals than radio waves? (1)
Hint: Uni-directional propagation.
10. What is the requirement of transmitting microwaves from one to another on the earth?
Ans: The transmitting and receiving antennas must be in line of sight. (1)
11. Name the type of radio wavespropagationinvolvedwhenTV signals broadcast by a tall antenna are
intercepted directly by the receiver antenna. (1)
12. Why sky waves are not used for the transmission of TV signals? (1)

13. A TV tower has a height of 300m. What is the maximum distance upto which this TV transmission
can be received?
Ans: d = √2Rh = √ 2 x 6400 x 1000 x 300 = 62km (1)
14. How does the effective power radiated by an antenna vary with wavelength? (1)
15.*Why ground wave propagation is not suitable for high frequency? (OR)Why is ground wave
propagation restricted to frequency up to 1500 kHz? (1)
Hint: It is because radio waves having frequency greater than 1500MHz are strongly absorbed by the
ground.
16.*Why are signals not significantly absorbed by ionosphere in satellite communication?
Hint: It is because satellite communication employs HF carrier i.e. microwaves (1)
17. How manygeostationarysatellitesare requiredtoprovide communicationlinkoverthe entire globe
and how should they be parked? (1)
18.* Why is the orbit of a remote sensing satellite called sun synchronous? (1)
Hint: itis because wheneversuchasatellitespassesover a particular area of the Earth, the position of
the sun with respect to that area remains the same.
19.At a particular place at a distance of 10km from a transmission station a person can receive signals
but notable to receive signalsat 100km, suggest a method how he can receive signal at 11 km By using
antenna. (1)
20. The tuned circuit of oscillator in a single AMtransmitter employs 50 uH coil and 1nF capacitor. The
oscillator output is modulated by audio frequency up to 10KHz. Determine the range of AM wave.
(2)
Hint: υc = 1/2π√LC ; USF = υc + υm ; LSF = υc – υm
21. The TV transmissiontowerata particularstationhasa heightof 160 m. What isthe Coverage range?
(2)
22. What is the population covered by the transmission, if the average Population density around the
tower is 1200km-2
? (2)
Hint: d = √2Rh=√2×6.4×103
×160×10-3
=45km Range 2d=2×45=90km
Population covered=area × population density=1200×6359= 763020
23. A transmitting antenna at the top of tower has a height of 36m and the height of the receiving
antenna is 49m. What is the maximum distance between them, for the satisfactory communication in
the LOS mode? (Radius of the earth =6400km). (2)
Hint. Using d= √2Rht + √2Rhr we get =46.5km
24. Derive an expression for covering range of TV transmission tower (2)
25. * What is space wave propagation? Which two communication methods make use of this mode of
propagation? If the sum of the heights of transmitting and receiving antennae in line of sight of
communicationisfixedat h,showthat the range ismaximumwhen the twoantennae have aheighth/2
each. (3)
Ans: Satellite communication and line of sight (LOS) communication make use of space waves.
Here d1=√2Rh2 and d2= √2Rh2
For maximum range,
Dm=√2Rh1 + √2Rh2
where dm =d1 + d2= d
Given h1 + h2 = h
Let h1 = x then h2 = h-x
Then dm = √2Rx + √2R(h-x) ,
d dm /dx = √R/2x - √R/2(h-x) = 0
i.e., 1/2x = 1/2(h-x) i.e., x = h/2
=> h1 = h2 = h/2.

26. * A ground receiver station is receiving signals at (i) 5 MHz and (ii) 100 MHz, transmitted from a
groundtransmitterat a heightof 300 m locatedat a distance of 100km. Identifywhetherthe signals are
coming via space wave or sky wave propagation or satellite transponder. Radius of earth = 6400 km;
Maximum electron density in ionosphere, Nmax = 1012
m-3
(3)
Solution:
Maximum coverage range of transmitting antenna, d = √2Reh
Therefore d = √2 x 6400 x 103
x 300 = 6.2 x 104
The receiving station (situated at 100 km) is out of coverage range of transmitting antenna, so space
wave communication is not possible, in both cases (i) and (ii) The critical frequency (or maximum
frequency) of ionospheric propagation is fc = 9(Nmax)1/2
= 9 x √1012
= 9 x 106
Hz = 9 MHz Signal (i) of
5MHz (< 9 MHz) is comingviaionosphere mode or sky wave propagation, while signal (ii) of 100MHz is
coming via satellite mode.
27. * Bywhat percentage will the transmission range of a TV tower be affected when the height of the
tower is increased by 21%. ? (3)
Solution:
Transmission range of TV tower = d = √2hR If the height is increased by 21%, new height
h’ = h + 21100h = 1.21h
If d’ is the new average range, then d’/d =√h’ / √h = 1.1% increase in range Δd d x 100% = (d’ – d d) x
100% = (d’/ d -1) x100% = (1.1 – 1) x 100% = 10%
MODULATION
1. What type of modulation is used for commercial broadcast of voice signal? (1)
2. *Over modulation result in distortion of the signal in amplitude modulation. Why? (1)
Ans: Whencarrier wave isovermodulated(i.e.ma>1),the modulatedwave will be absent at negative peak
of modulating signal. This results in distortion of the signal.
3.*An AM wave contains more power than the carrier wave. Why? (1)
Ans: An AMwave containsthree components, the carrier components and the two side band components
(LSB and USB). It therefore contains more power than the carrier wave.
4.* Why is frequency modulation better than amplitude modulation? (1)
5.* What would be the modulation index for an amplitude modulated wave for which the maximum
amplitude is ‘a’ while the minimum amplitude is ‘b’? (2)
Ans. Modulation index, am = Em/Ec … (1)
Maximum amplitude of modulated wave a=Ec + Em .....(2)
Minimum amplitude of modulated wave b = Ec - Em …(3)
From (2) and (3), Ec = a+b/2, Em = a-b/2
From (1), modulation index, am = Em/Ec = (a-b)/2 / (a+b)/2 = a-b/ a+b
6. A carrier wave of peak voltage 20 V is used to transmit a message signal. What should be the peak
voltage of the modulating signal, in order to have a modulation index of 80% ? (2)
Hint: Modulation index, ma = Em / Ec
Em =ma x Ec = 0.80 x 20 V = 16 V
7. A message signal of frequency 10 kHz and peak value of 8 volts is used to modulate a carrier of
frequency 1MHz and peak voltage of 20 volts. Calculate: (i) Modulation index
(ii) The side bands produced. (2)
Solution: (i) Modulation index, ma = Em / Ec = 8/20 = 0.4
(ii) Side bands frequencies = fc ± fm
Thus the side bands are at 1010KHz and 990 kHz.
8.An amplitude modulation diode detector, the output circuit consists of resistance R = 1kΩ and
capacitance C = 10pf. It isdesired to detect a carrier signal of 100 kHz by it. Explain whether it is a good
detector or not? If not what value of capacitance would you suggest? (3)
Solution: The satisfactory condition for demodulation is that reactance at carrier frequency must be

much less than R.
Reactance = 1 / ώC = 1 / 2πfCC = 1/ 2 x 3.14 x 100 x 103
x 10 x 10-12
= 1.59 x 105 Ω = 159 kΩ
This ismuch greaterthanthe givenresistance,soitisnot a good detector.For detection, the condition
is 1 / 2πfCC << R = C >> 1 / 1.59 x 10-9
fared or C >> 1.59 nF.
Thus for proper detection the capacitance of output circuit must be much greater than 1.59 nF. The
suitable capacitance is 1µF.

FREQUENTLY ASKED QUESTIONS
UNIT I
ELECTROSTATICS
2 MARKS
1) Force of attraction between two point charges placed at a distance of‘d’ is ‘F’. What
distance aparttheyare keptinthe same medium, sothat, the force between them is ‘F/3’?
2) Define electricfieldintensity.Write itsSIunit.Write the magnitude anddirectionof electric
field intensity due electric dipole of length 2a at the midpoint of the line joining the two
charges.
3) Define electricfieldintensity.Write itsS.Iunit.Write the magnitudeanddirectionof electric
field intensity due to an electric dipole of length2a at the midpoint of the line joining the
two charges.
4) Sketch the electric lines of force due to point charges q > 0, q < 0 and for uniform field.
5) Define electric flux. Give its S.I unit and dimensional formula.
6) Two point charges 4μc and -2μc are separated by a distance of 1 m in air. At what point on
the line joining the charges is the electric potential zero?
7) Depictthe equipotential surfacesforasystemof two identical positive point charges placed
at distance d apart.
8) Deduce the expressionforthe potential energy of a system of two point charges q1 and q2
brought from infinity to that points r1 and r2.
3 MARKS
9) Derive an expression for electric field intensity at a point on the axial line and on the
equatorial line of an electric pole.
10) Derive an expression for torque acting on an electric dipole in a uniform electric filed.
11) Derive anexpressionfortotal workdone inrotatingan electricdipole throughanangle ‘θ’in
uniform electric field.
12) A sphere ‘S1’ of radius ‘r1’ encloses a charge ‘Q’. If there is another concentric sphere S2 of
the radiusr2 (r2 > r1) and there be no additional charges between S1 and S2, find the ratio
of electric flux through S1 and S2.
13) State Gauss’sTheoreminelectrostatics.Using this theorem, find the electric field strength
due to an infinite plane sheet of charge.
14) State Gauss' theorem. Apply this theorem to obtain the expression for the electric field
intensity at a point due to an infinitely long, thin, uniformly charged straight wire.
15) . UsingGauss’s theorem,show mathematicallythatforanypointoutside the shell, the field
due to a uniformlycharged thinspherical shellisthe same asif the entire charge of the shell
isconcentratedat the centre.Whydo you expectthe electricfieldinside the shell tobe zero
according to this theorem?
16) Deduce an expressionforthe electricpotential due to an electric dipole at any point on its
axis. Mention one contrasting feature of electric of a dipole at a point as compared to that
due to single charge.
17) Define dielectric constant in terms of the capacitance of a capacitor.
5 MARKS
18) Give the principle and working of a Van de Graff generator. With the help of a labelled
diagram, describe its construction and working. How is the leakage of charge minimised
from the generator?
19) Briefly explain the principle of a capacitor. Derive an expression for the capacitance of a
parallel plate capacitor, whose plates are separated by a dielectric medium.
20) Derive anexpressionforthe energystoredinaparallel plate capacitorwithairbetweenthe
plates. How does the stored energy change if air is replaced by a medium of dielectric
constant ‘K’? ; Also show that the energy density of a capacitor is.

21) A parallel-platecapacitorischargedto a potential difference V bya dc source. The capacitor
isthendisconnected from the source. If the distance between the plates is doubled, state
with reason how the following change
(i) electric field between the plates
(ii) capacitance, and
(iii) energy stored in the capacitor
22) Explainthe underlyingprinciple of workingof aparallel plate capacitor.If twosimilarplates,
each of area ‘A’havingsurface charge densities‘+σ’ & ‘-σ’ are separatedby a distance ‘d’ in
air, write expressions for (i) the electric field at points between the two plates, (ii) the
potential difference between the plates & (iii) the capacity of the capacitor so formed
23) A parallel plate capacitor is charged by a battery and the battery remains connected, a
dielectric slab is inserted in the space between the plates. Explain what changes if any ,
occur in the values of
(I) potential difference between the plates
(II) electric field between the plates
(III) energy stored in the capacitor.
UNIT II
CURRENT ELECTRICITY
2 MARKS
1. Two wires ‘A’ & ‘B’ are of the same metal and of the same length. Their areas of cross-section
are inthe ratio of 2:1. if the same potential difference is applied across each wire in turn, what
will be the ratio of the currents flowing in ‘A’ & ‘B’?
2. Explain,with the help of a graph, the variation of conductivity with temperature for a metallic
conductor.
3. Draw V-I graph for ohmic and non-ohmic materials. Give one example for each.
4. Explain how does the resistivity of a conductor depend upon (i) number density ‘n’ of free
electrons, & (ii) relaxation time‘t’.
5. Define the term ‘temperature coefficient of resistivity’. Write its SI unit. Plot a graph showing
the variation of resistivity of copper with temperature.
6. A cell of emf (E) and internal resistance (r) is connected across a
variable external resistance (R) Plot graphs to show variation of (i) E
with R (ii) terminal p.d. of the cell (V) with R.
7. Explain how electron mobility changes from a good conductor
(i) when temperature of the conductor is decreased at constant
potential difference and (ii) applied potential difference is doubled
at constant temperature.
8. Write the mathematical relation between mobility and drift velocity of charge carriers in a
conductor.Name the mobile charge carriersresponsible forconductionof electric current in: (i)
an electrolyte, & (ii) an ionised gas.
9. Define drift velocity. Establish a relation between current & drift velocity.
10. Define the termcurrentdensityof ametallicconductor.Deduce the relationconnecting current
density ‘J’ & the conductivity ‘σ’ of the conductor when an electric field ‘E’ is applied to it.
11. Why do we prefer potentiometer to compare the e.m.f of cells than the voltmeter. Why?
12. State Kirchhoff’s rules of current distribution in an electric network.
13. The variationof potential difference “V’ with length ‘l’ in the case of two potentiometers ‘X’ &
‘Y’ isas showninfigure.Whichone of these twowill youpreferforcomparing‘emf’sof twocells
and why?
X
V
Y

3 MARKS
14. Draw a circuit diagramusinga metre bridge andwrite the necessarymathematical relationused
to determine the valueof anunknownresistance.Whycannotsuchan arrangementbe used for
measuring very low resistance?
15. Withthe helpof a circuitdiagram, explaininbrief the use of apotentiometer for comparison of
‘emf’s of two cells.
16. Prove that the currentdensityof a metallicconductorisdirectly proportional to the drift speed
of electrons.
17. A number of identical cells, n, each of emf E, internal resistance r connected
in series are charged by a d.c. source of emf E′, using a resistor R.
(i) Draw the circuit arrangement.
(ii) Deduce the expressions for (a) the charging current and (b) the potential difference
across the combination of the cells.
18. Derive the principle of wheatstone bridge using Kirchoff’s law.
19. State Kirchhoff’s rules of current distribution in an electrical network.
Using these rules determine the value of the current I1 in the electric circuit given below.
20. Write the mathematical relation for the resistivity of material in terms of
relaxationtime,numberdensity and mass and charge of charge carriers in it.Explain, using this
relation,whythe resistivityof ametal increasesandthatof semi-conductor decreases with rise
in temperature.
21. Calculate the value of the resistance R in the circuit shown in the figure so that the current in
the circuit is 0·2 A. What would be the potential difference between points A and B?
UNIT III
MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
2 MARKS
1. A circular coil of radius ‘R’ carries a current ‘I’. Write the expression for the magnetic field
due to this coil at its centre. Find out the direction of the magnetic field.
2. Write the expression for the force on the charge moving in a magnetic field. Use this
expression to define the SI unit of magnetic field.

3. Define magnetic susceptibility of a material. Name two elements, one having positive
susceptibilityandthe otherhavingnegative susceptibility.Whatdoesnegative susceptibility
signify?
4. Define the term magnetic dipole moment of a current loop. Write the expression for the
magnetic moment when an electron revolves at a speed around an orbit of radius in
hydrogen atom..
5. Explainwiththe helpof adiagram the term ‘magnetic declination’ at a given place.
6. Define the term ‘angle of dip’. What is the value of the angle of dip at the magnetic
equator? What does it mean?
7. Two wires of equal lengths are bend in the form of two loops. One of the loop is square
shapedwhere asthe otherloopiscircular. These are suspendedinauniformmagnetic field
and the same current is passed through them. Which loop will experience greater torque?
Give reasons.
8. Explainwhysteel ispreferredformakingpermanentmagnets whilesoftironispreferredfor
making electromagnets.
9. Draw diagram to show behavior of magnetic field lines near a bar of 1)copper2)aluminum
and3)mercury cooled at a very low temperature(4.2K)
10. How will the magnetic field intensity at the centre of the circular coil carrying current will
change, if the current through the coil is doubled and radius of the coil is halved?
11. What do you mean by current sensitivity of a moving coil galvanometer? On what factors
does it depend?
12. Derive an expression for the force experienced by a current carrying straight conductor
placed in a magnetic field. Under what condition is this force maximum?
3 MARKS
13. Obtain the force per unit length experienced by two parallel conductors of infinite length
carrying current in the same direction. Hence define one ampere.
14. A) If Ҳ -stands for the magnetic susceptibility of a given material, identify the class of
materials for which (a) -1 ≥ Ҳ < 0, and (b) 0 < Ҳ < έ [έ is a small positive number]. Write the
range of relative magnetic permeability of these materials.
B) Draw the patternof the magneticfieldlineswhenthese materials are placed on a strong
magnetic field.
15. Derive anexpressionforthe force actingon a current carryingconductorin a magneticfield.
Under what conditions this force is maximum and minimum?
16. Define the termmagneticmomentof current loop. Derive the expression for the magnetic
moment when an electron revolves at a speed ‘v’ around an orbit of radius r in hydrogen
atom.Also calculate the value of Bohr’smagnetic moment.
17. With the help of diagram explain how a galvanometer can be converted into an ammeter
and a voltmeter.
18. To increase the current sensitivity of a moving coil galvanometer by 50%, its resistance is
increased so that the new resistance becomes twice its initial resistance. By what factor
does its voltage sensitivity change?
5 MARKS
19. Write an expression for force experienced by a charged particle moving in a uniform
magnetic field? With the help of labeled diagram, explain principle and working of a
cyclotron. Show that cyclotron frequency does not depend upon the speed of particles.
Write its two limitations.
20. State Ampere’sCircuital Law. Derive an expression for the magnetic field at a point due to
straight current carrying conductor.
21. Derive anexpressionforthe magneticfieldata pointalongthe axis of an air cored solenoid
using a Ampere’s circuital law..

22. Derive an expression for torque acting on a rectangular current carrying loop kept in a
uniform magnetic field B. Indicate the direction of torque acting on the loop.
23. With neat diagram, describe the principle, construction and working of a moving coil
galvanometer. Explain the importance of radial field.
24. State Biot Savart Law. Use this law to obtain a formula for magnetic field at the centre of a
circular loop of radius R ,number of turns N carrying current I. Sketch the magnetic field
lines for a current loop clearly indicating the direction of the field.
25. Distinguish the magneticpropertiesof dia, para- and ferro-magnetic substances interms of
(i) susceptibility,(ii) magneticpermeabilityand(iii) coercivity. Give one example of each of
these materials.Draw the field lines due to an external magnetic field near a (i)
diamagnetic,(ii) paramagnetic substance.
UNIT IV
ELECTROMAGNETIC INDUCTION &
ALTERNATING CURRENT
2 MARKS
1. How doesthe self-inductance of anair core coil change,when(i) the numberof turnsin the coils
is decreased & (ii) an iron rod is introduced in the coil.
2. What is the effect on the mutual inductance between the pair of coil when
(i) the distance betweenthe coilsisincreased?(ii) the numberof turnsineach coil isdecreased?
Justify your answer in each case.
3. State Lenz’s law. Show that it is in accordance with the law of conservation of energy.
4. The closedloopPQRSis movingintoauniformmagneticfieldacting at right angles to the plane
of the paper as shown. State the direction of the induced current in the loop.
x x x x x
P Q
x x x x x
x x x x x
x x x x x
x x x x x
S R R
x x x x x
5. Define mutual inductance and give its S.I. unit.Write two factors on which the mutual-
inductance between a pair of coil depends.
6. What isthe powerdissipatedin an ac circuit in which voltage & current are given by V = 230 sin
(ωt + π/2) and I = 10 sin ωt?
7. The instantaneous current & voltage of an ac circuit are given by:
i = 10 sin 314t ampere, & V = 50 sin 314t volt.
What is the power dissipation in the circuit?
8. The coilsin certaingalvanometershave fixedcore made of a non-magnetic material. Why does
the oscillating coil come to rest so quickly in such a core?
9. What are eddycurrents.Howare these produced? in what sense are eddy currents considered
undesirable in a transformer and how are these reduced in such a device?
10. Prove that average power consumed over a complete cycle of ac through an ideal inductor is
zero.

11. Prove that an ideal capacitor in an ac circuit does not dissipate power.
12. Distinguish resistance,reactance and impedance.
13. What is an induced emf? Write Faraday’s law of electromagnetic induction Express it
mathematically.
14. Two identical loops, one of copper and the other of aluminum, are rotated with the same
angular speed in the same magnetic field. Compare (i) the induced emf and (ii) the current
produced in the two coils. Justify your answer.
3 MARKS
15. Derive an expression for: (i) induced emf & (ii) induced current when, a conductor of length is
moved into a uniform velocity v normal to a uniform magnetic field B. Assume resistance of
conductor to be R.
16. Derive an expression for average power consumed over a complete cycle of ac through an LCR
circuit.
17. Define mutual inductanceandgive itsSIunit.Derive anexpressionforthe mutual inductance of
two long coaxial solenoids of same length wound over the other.
18. . Define self-inductance andgive itsS.I.Unit. Derive anexpressionforself-inductance of a long,
air-cored solenoid of length l, radius r, and having N number of turns
5 MARKS
19. Explain the term 'capacitive reactance'. Show graphically the variation of capacitive reactance
withfrequency of the applied alternating voltage.An a.c. voltage E=E0sinωt is applied across a
pure capacitor of capacitance C. Show mathematically that the current flowing through it leads
the applied voltage by a phase angle of π/2. .
20. Explain the term 'inductive reactance'. Show graphically the variation of inductive reactance
with frequency of the applied alternating voltage.
An a.c. voltage E=E0 sinωt is applied across a pure inductor of inductance L. Show
mathematically that the current flowing through it lags behind theapplied voltage by a phase
angle of π/2.
21. An AC source of voltage V = Vm sin ωt is applied across a series LCR circuit. Draw the phasor
diagrams for this circuit, when:
a) Capacitive impedance exceeds the inductive impedance AND
b) Inductive impedance exceeds capacitive impedance.
22. A coil of inductance ‘L’,a capacitorof capacitance ‘C’,& a resistorof resistance ‘R’are all put in
serieswithan alternating source of emf E = E0 sin ωt. Write expressions for a) total impedance
of circuit, and (b) frequency of source emf for which circuit will show resonance.
23. A circular coil of N-turns & radius ‘R’ is kept normal to a magnetic field, given by: B = B0 cos ωt.
Deduce an expressionfor the emf induced in this coil. State the rule which helps to detect the
direction of induced current.
24. Discuss a series resonant circuit. Derive an expression for resonant frequency and show a
graphical variationbetween current and angular frequency of applied ac. Define quality factor
and derive an expression for it.
25. Explainwithhelpof alabelleddiagramthe principle, constructionandworkingof a transformer.
Mention the various energy losses in a transformer? Explain the role of transformer in long
distance transmission of power ?
26. With the help of a neat diagram, explain the principle construction and working of an a.c
generator.

UNIT V
ELECTROMAGNETIC WAVES
2 MARKS
1. A plane monochromatic light wave lies in the visible region. It is represented by sinusoidal
variation with time by the following components of electric field:
EX = 0, EY = 4 sin [2π/λ (x – vt)], Ez = 0
Where, v = 5 x 1014
Hz and λ is the wave length of light.
(i) What is the direction of propagation of the wave?
(ii) What is its amplitude? And
(iii) Compute the components of magnetic field.
2. Give two characteristics of electromagnetic waves. Write the expression for the velocity of
electromagnetic waves in terms of permittivity and magnetic permeability of free space.
3. Find wavelength of electromagnetic waves of frequency 5 x 1019
Hz in free space. Give its two
applications.
4. Name the characteristics of e. m. waves that: (i) increases, & (ii) remains constant in e. m.
spectrum as one moves from radiowave region towards ultraviolet region.
3 MARKS
5. Whichconstituentradiationof electromagneticspectrumisused:(i) inradar?(ii) Tophotograph
internal parts of human body? & (iii) for taking photographs of the sky during night and foggy
condition? Give one reason for your answer in each case.
6. Write any four characteristics of e. m. waves. Give two uses of: (i) Radio waves & (ii)
Microwaves.
7. Name the followingconstituentradiationsof e.m.spectrumwhich, (i) produce intense heating
effect? (ii) is absorbed by the ozone layer, &(iii) is used for studying crystal structure.
8. Experimentalobservationshave shown:(i) thatX-raystravel invacuumwithaspeedof 3 x 108
m
s-1
,& (ii) the phenomenonof diffraction and can be polarized. What conclusion is drawn about
the nature of X-rays from each of these observations?
9. Why are infrared radiations referred to as heat waves? Name the radiations which are next to
these radiations in e. m. spectrum having: (i) shorter wavelength, & (ii) longer wavelength.
10. The oscillating magnetic field in a plane electromagnetic wave is given by:
By = 8 x 10-6
sin [2 x 1011
t + 300 π x] T
(i) Calculate the wavelength of the electromagnetic wave &
(ii) Write down the expression for oscillating electric filed.
11. Identify the following electromagnetic radiation as per the wavelengths given below:
(a) 10-3
nm, & (b) 10-3
m, & (c) 1 nm; Write
one application of each.
12. Name the constituent radiation of electromagnetic spectrum which
(a) is used in satellite communication.
(b) is used for studying crystal structure.
(c) is similar to the radiations emitted during decay of radioactive nuclei.
(d) has its wavelength range between 390 nm and 770 nm.
(e) is absorbed from sunlight by ozone layer.
(f) produces intense heating effect.
13. What is meant by the transverse nature of electromagnetic waves? Drawdiagram showing the
propagation of the an electromagnetic wave along X direction, indicating clearly the directions of
oscillating electric and magnetic fields associated with it.

UNIT VI
OPTICS
2 MARKS
1. What is the geometrical shape of the wavefront when a plane wave passes through a
convex lens?
2. What is total internal reflection? Under what condition does it take place.
3. A convex lens made up of a material of refractive index n1, is immersed in a medium of
refractive index n2.Trace the pathof a parallel beamof lightpassingthroughthe lenswhen:
(i) (i) n1> n2, (ii) n1 = n2, & (iii) n1< n2..Explain your answer.
4. A concave lens made of material of refractive index n1 is kept in a medium of refractive
index n2.A parallel beam of light is incident on the lens. Complete the path of rays of light
emergingfromthe concave lensif:(i) n1>n2,(ii) n1 = n2, & (iii) n1<n2.
5. Draw a ray diagram to showhow an image is formed by a compound microscope. ?
6. A microscope is foucssed on a dot at the bottom of a beaker. Some oil is poured into the
beaker to a height of ‘y’ cm & it is found necessary to raise microscope through a vertical
distance of ‘x’cm to bringthe dot againintofocus.Expressrefractive indexof oil in terms of
‘x’ & ‘y’.
7. How does the (i) magnifying power & (ii) resolving power of a telescope change on
increasing the diameter of its objective? Give reasons for your answer.
8. How will magnifying power of a “refracting type astronomical telescope” be affecting on
increasing for its eye piece: (i) the focal length, & (ii) the aperture. Justify your answer.
9. Draw a labelled ray diagram showing the formation of image of a distant object using an
astronomical telescope in the ‘normal adjustment position’
10. Draw a labelled ray diagram showing the formation of image of a distant object using an
astronomical telescope in the near point adjustment.
11. Draw a ray diagram to illustrate imageformationbya Cassegrain type reflecting telescope.
12. Explain with reason, how the resolving power of an astronomical telescope will change
when(i) frequencyof the incidentlightonobjectivelensis increased (ii) the focal length of
the objective lens is increased & (iii) aperture of the objective lens is halved.
13. Draw a graph to showvariationof angle of deviation‘D’withthatof angle of incidence ‘i’for
a monochromatic ray of light passing through a glass prism of reflecting angle ‘A’.
3 MARKS
14. Derive lens/mirror formula in case of a convex/concave mirror.
15. Statingthe assumptionsandsignconventions, derive expression for lens maker’s formula.
16. A right-angled crown glass prism with critical angle 41○
is placed before an object, ‘PQ’ in
two positions as shown in the figures (i) & (ii). Trace the paths of the rays from ‘P’ & ‘Q’
passing through the prisms in the two cases.
17. (a) Draw a labelled ray diagram to show the formation of an image by a compound
microscope. Write the expression for its magnifying power.
18. (b) Define resolving power of a compound microscope.

How doesthe resolvingpowerof acompoundmicroscope change,when(i) refractive index
of the mediumbetweenthe objectand the objective lens increases and (ii) Wavelength of
the radiation used is increased?
19. Define the term wave front? Using Huygen’s construction draw a figure
showing the propagation of a plane wave reflecting at the interface
of the two media. Show that the angle of incidence is equal to the
angle of reflection.
20. Define the term ‘wavefront’. Draw the wavefront and corresponding
rays in the case of a (i) diverging spherical wave (ii) plane wave.
Using Huygen’s construction of a wavefront, explain the refraction of
a plane wavefront at a plane surface and hence deduce Snell’s law.
21. What ismeantby ‘interference of light’? Write any two conditions necessary for obtaining
well-defined and sustained interference pattern of light.
22. What is the effect on the interference fringes in a Young’s double slit experiment due to
each of the followingoperations?Give reasonforyour answer: (i) Separation between two
slits is increased & (ii) monochromatic source is replaced by a source of white light.
23. Draw the curve depicting variationof intensityinthe interference patterninYoung’sdouble
slit experiment. State conditions for obtaining sustained interference pattern of light.
24. In a single slitdiffractionpattern,how is angular width of central bright maximum changed
when (i) the slit width is decreased, (ii) the distance between the slit and the screen is
increased,&(iii) light of smaller wavelength is used? Justify your answers.
25. Why is diffraction of sound waves easier to observe than diffraction of light waves? What
two main changes in diffraction pattern of a single slit will you observe when the
monochromatic source of light is replaced by a source of white light?
26. In a single slit diffraction experiment, if the width of the slit is doubled, how does the (i)
intensity of light and (ii) width of the central maximum change? Give reason for your
answer.
27. What iswavefront?Whatis the geometrical shape of a wavefront emerging from a convex
lens when point source is placed at the focus?
28. What is wavefront? Distinguish between a plane wavefront and a spherical wavefront.
Explain with the help of a diagram, the refraction of a plane wavefront at a plane surface
using Huygens’s construction.
29. Using Huygens’s principle show that for parallel beam incident on a reflecting surface the
angle of reflection is equal to the angle of incidence.
30. Distinguishbetweenunpolarisedandplane polarised light. An unpolarised light is incident
on the boundary between two transparent media. State the condition when the reflected
wave is totally plane polarised. Find out the expression for the angle of incidence in this
case.
31. The followingdatawasrecordedforvaluesof objectdistance andthe corresponding values
of image distance in the experiment on study of real image formation by a convex lens of
power +5D. One of the observations is incorrect. Identify the observation and give reason
for your choice.
S. No. 1 2 3 4 5 6
Objectdistance (cm) 25 30 35 45 50 55
Image distance (cm) 97 6 37 35 32 30
5 MARKS
32. (i) Derive the mirror formula which gives the relation between f, v and u. What is the
correspondingformulaforathinlens? (ii) Calculatethe distance d,sothata real image of an
object at O, 15cm in front of a convex lens of focal length 10cm be formed at the same
pointO.The radiusof curvature of the mirror is 20cm. Will the image be inverted or erect?

33. A spherical surface of radius of curvature ‘R’ separates a rarer and a denser medium as
shown in the figure.
Complete the path of the incident ray of light, showing the formation of
real image. Hence derive the relation connecting object distance ‘u’,
image distance ‘v’ radius of curvature ‘R’ and the refractive indices ‘n1’ & ‘n2’ of the media.
Briefly explain how the focal length of a convex lens changes with
Increase inwavelengthof incidentlight.
34. State the assumptionsandsign conventions in deriving the Lens maker’s formula and also
derive an expression for it.
35. Derive an expression for thin lens formula.
36. (a) In Young’s double slit experiment, deduce the conditions for: (i) constructive and (ii)
destructive interference at a point on the screen. Draw a graph showing variation of the
resultant intensity in the interference pattern against position ‘x’ on the screen.
(b) Compare andcontrast the patternwhichis seenwithtwocoherentlyilluminated narrow
slitsinYoung’sexperimentwiththatseenforacoherently illuminated single slit producing
diffraction.
37. State Huygensprinciple. Usingthe geometrical constructionof secondarywavelets, explain
the refraction of a plane wavefront incident at a plane surface. Hence verify Snell’s law of
refraction.Illustratewiththe helpof diagramsthe actionof:(i) convex lens and (ii) concave
mirror on a plane wavefront incident on it.
38. What is interference of light? Write two essential conditions for sustained interference
pattern to be produced on the screen. Draw a graph showing the variation of intensity
versusthe positiononthe screeninYoung’sexperimentwhen (a) both the slits are opened
and (b) one of the slit is closed. What is the effect on the interference pattern in Young’s
double slitexperimentwhen: (i) Screenismovedcloserto the plane of slits? (ii)Separation
between two slits is increased. Explain your answer in each case.
39. What are coherent sources of light? Two slits in Young’s double slit experiment are
illuminatedbytwodifferentsodiumlampsemittinglightof the same wavelength.Why is no
interference pattern observed?
(b) Obtain the condition for getting dark and bright fringes in Young’s experiment. Hence
write the expression for the fringe width.
(c) If S isthe size of the source and its distance from the plane of the two slits, what should
be the criterion for the interference fringes to be seen?
40. What do we understand by ‘polarization of wave’? How does this phenomenon help us to
decide whether a given wave is transverse or longitudinal in nature?
41. Light from an ordinary source (say, a sodium lamp) is passed through a Polaroid sheet ‘P1’.
The transmittedlightisthenmade topass througha second Polaroid sheet P2 which can be
rotated so that the angle θ between the two Polaroid sheets varies from 0●
to 90●
. Show
graphicallythe variationof intensityof light,transmittedbyP1&P2 as a functionof the angle

θ. Take the incidentbeamintensityaI0. Why does the light from a clear blue portion of the
sky, show a rise and fall of intensity when viewed through a Polaroid which is rotated?
42. (a) Draw a ray diagram to show the refraction of light through a glass prism. Hence obtain
the relationforthe angle of deviationintermsof the angle of incidence,angleof emergence
and the angle of the prism. (b) A right angled isosceles glass prism is made from glass of
refractive index When a monochromatic yellow coloured light beam is incident on a given
photosensitive surface, photoelectrons are not ejected, while the same surface gives
photoelectronswhenexposedtogreencolouredmonochromaticbeam.Whatwill happenif
the surface is exposed to: (i) red coloured, monochromatic beam of light? Justify your
answer.
UNIT VII
DUAL NATURE OF MATTER
2 MARKS
1. When a monochromatic yellow coloured light beam is incident on a given photosensitive
surface, photoelectrons are not ejected, while the same surface gives photoelectrons when
exposedtogreencolouredmonochromaticbeam.Whatwill happen if the surface isexposedto:
(i) red coloured, monochromatic beam of light? Justify your answer.
2. What ismeantby workfunctionof a metal?How doesthe value of work function influence the
kinetic energy of electrons liberated during photoelectric emission?
3. Define the terms: (i) work function, (ii) threshold frequency & (iii) stopping potential with
reference of photoelectric effect.
4. The work function of lithium is 2.3 eV. What does it mean? What is the relation between the
work function ‘ωo’ and threshold wavelength ‘λo’ of a metal?
5. Red light, however bright, cannot cause emission of electrons from a clean zinc surface. But,
even weak ultraviolet radiations can do so. Why?
6. An electronanda protonhave same kineticenergy.Whichof the twohasa greaterwavelength?
Explain.
7. Define the term threshold frequency & work function in relation to photoelectric effect.
8. An electron and a proton are moving in the same direction and possess same kinetic energy.
Find the ratio of de-Broglie wavelengths associated with these particles.
9. In the photoelectric effect experiment, the graph between the stopping potential ‘V’ and
frequency ‘v’ of the incident radiation on two different metal plates P and Q are shown in the
figure.(i) Whichof the twometal plates,P& Q has greatervalue of work function? & (ii) What
does the slope of the line depict?
3 MARKS
10. What isphotoelectriceffect?Write Einstein’s photoelectric equation and use it to explain: (i)
independence of maximum energy of emitted photoelectrons from the intensity of incident
light. (ii) Existence of a threshold frequency for the emission of photoelectrons.
11. Draw the variation of maximum kinetic energy of emitted electrons with frequency of the
incident radiation on a photosensitive surface. On the graph drawn, what do the following
indicate: (i) slope of the graph & (ii) intercept on the energy axis.

12. ObtainEinstein’sphotoelectricequation. Explain how it enables us to understand the (i) linear
dependence of the maximumkinetic energy of the emitted electrons, on the frequency of the
incident radiation & (ii) existence of a threshold frequency for a given photo emitter.
13. Given below is the graph between frequency (v) of the incident light and maximum kinetic
energy(E) of emitted photoelectrons. Find the values of: (i) threshold frequency and (ii) work
function from the graph.
14. Sketch a graph between frequency of incident radiations and stopping potential for a given
photosensitivematerials.Whatinformationcanbe obtained from the value of intercept on the
potential axis?A source of lightof frequencygreaterthatthe thresholdfrequency is replaced at
a distance of 1 m fromthe cathode of a photocell.The stoppingpotentialisfoundtobe V.If the
distance of the lightsource fromthe cathode is reduced,explaingivingreason,whatchange you
will observe in the (I0 photoelectric current & (ii) stopping potential.
15. Explain the laws of photoelectric emission on the basis of Einstein’s photoelectric equation.
Write one feature of the photoelectric effect which cannot be explained on the basis of wave
theory of light.
16. Draw graphs showingthe variationof photoelectriccurrentwith anode potential of a photocell
for (i) the same frequencybutdifferentintensitiesI1>I2>I3 of incident radiation, & (ii) the same
intensity but different frequencies v1> v2> v3 of incident radiation. Explain why the saturation
current is independent of the anode potential?
UNIT VIII
ATOMS & NUCLEI
2 MARKS
1. Define disintegration constant and mean life of a radioactive substance. Give the unit of each.
2. What isimpact parameter? What is the value of impact parameter for a head on collision? The
sequence of the stepwise decays of radioactive nucleus is:
α β α α
D D1 D2 D3 D4.
If the nucleon number and atomic number for D2 are respectively 176 & 71, what are the
corresponding values for D and D4 nuclei? Justify your answer.
3. Draw a diagram to show the variation of binding energy per nucleon with mass number for
different nuclei. Explain with the help of this plot the release of energy in the processes of
nuclear fission and fusion?
4. The value of ground state energyof hydrogenatomis: -13.6 eV;(i) What does the negative sign
signify? & (ii) How much energy is required to take an electron in this atom from the ground
state to the first excited state?

5. Give one pointof difference between‘nuclearfission’ & ‘nuclear fusion’. Will neutron to proto
ratio increase or decrease in a nucleus when: (i) an electron, (ii) a positron is emitted?
6. Sketchthe graph showingthe variationof potentialenergyof apair of nucleons as a function of
theirseparation.Write three characteristicpropertiesof nuclearforce which distinguish it from
the electrostatic force.
7. State two characteristics of nuclear force. Why does the binding energy per nucleon decrease
with increase in mass number for heavy nuclei like 235
U?
8. State the condition for controlled chain reaction to occur in a nuclear reactor. Heavy water is
often used as a moderator in thermal nuclear reactors. Give reason.
9. Define activityof asubstance.State itsS.Iunit.Derive an expression for activity of a substance.
10. Define average or mean value of a radioactive substance, and derive an expression for it.
3 MARKS
11. State the basic postulates of Bohr’s atomic model & derive an expression for the energy of an
electron in any orbit of hydrogen atom.
12. Derive an expression for the radius of stationary orbit. Prove that the various stationary orbits
are not equally spaced.
13. Derive mathematical expressions for: (i) kinetic energy, & (ii) potential energy of an electron
revolving in an orbit of radius ‘r’; how does the potential energy change with increase in
principal quantum number (n) for the electron and why?
14. Define the decayconstant for a radioactive sample. Which of the following radiations α, β, & λ
rays are: (i) similartoX-rays?(ii) easilyabsorbed by matter? & (iii) similar in nature to cathode
rays?
15. Define the terms: half life period and decay constant of a radioactive sample. Derive the
relation between these terms.
16. In Rutherford’sscatteringexperiment,mentiontwo important conclusions which can be drawn
by studyingthe scatteringof α particlesbyanatom. Draw the schematic arrangement of Geiger
and Marsden experiment showing the scattering of α particle by a thin foil of gold. How does
one get the information regarding the size of the nucleus in this experiment?
17. Sketch the energy level diagram for hydrogen atom. Mark the transitions corresponding to
Lyman and Balmer series.
18. Prove that the instantaneousrate of change of the activityof a radioactive substance isinversely
proportional to the square of its half life.
(3)
UNIT IX
ELECTRONIC DEVICES
2 MARKS
1. How isa p-type semiconductorformed?Name the majoritycarriers in it. Draw the energy band
diagram of a p-type semiconductor.
2. How isan n-type semiconductorformed?Name the majoritycarriersinit.Draw the energyband
diagram of a n-type semiconductor.
3. With the help of a diagram, show the biasing of a light emitting diode (LED). Give its two
advantages over conventional incandescent lamps.
4. Draw a circuit diagram to show how a photodiode is biased. Draw its characteristic curves for
two different illumination intensities.
5. Give the logicsymbol foran ANDgate. Draw the outputwave formforinputwave forms for this
gate.
3 MARKS
6. What is rectification? How can a diode valve be used as half wave rectifier and full wave
rectifier?
7. Explain how the depletion layer and the barrier potential are formed in a p-n junction diode.

8. Draw a circuit diagram for use of NPN transistor as an amplifier in common emitter
configuration. The input resistance of a transistor is On changing its base
current by , the collector current increases by 2 m A. If a load resistance of
is used in the circuit, calculate (i) the current gain & (ii) voltage gain of the
amplifier
9. The output of an AND gate is connected to both the inputs of a NAND gate. Draw the logic
circuit of this combination of gates and write its truth table.
10. What is a Zener diode? How it is symbolically represented? With the help of a circuit diagram,
explain the use of Zener diode as a voltage stabilizer.
11. Withthe helpof a suitable diagram, explainthe formationof depletion region in a p-n junction.
How does its width change when the junction is: (i) forward biased? & (ii) reverse biased?
5 MARKS
12. With the help of a circuit diagram explain the working of a transistor as an oscillator.
13. Explainbrieflywiththe help of a circuit diagram how V-I characteristics of a p-n junction diode
are obtained in: (i) forward bias & (ii) reverse bias.
14. Explain the function of base region of a transistor. Why this region is made thin and lightly
doped? Draw a circuit diagram to study the input and the output characteristics of n-p-n
transistor in a common emitter (CE) configuration. Show these characteristics graphically.
Explain how current amplification factor of the transistor is calculated using output
characteristics.
15. Draw the energybandsof p-type andn-type semiconductors. Explain with a circuit diagram the
working of a full wave rectifier.
16. Explain with the help of a circuit diagram the use of an n-p-n transistor as an amplifier in
commonemitterconfiguration.Draw the input and output wave forms of the signal. Write the
expression for its voltage gain.
17. What isan n-p-ntransistor?How doesitdifferfromp-n-ptransistor?Give theirsymbols.Explain
transistor action.
18. Explain the working of transistor as a switch. Draw transfer characteristic curve by showing 1)
Cutoff region 2) Active region and 3) Saturation region.
UNIT X
COMMUNICATION SYSTEMS
2MARKS
1. Draw a block diagram of communication system.
2. Distinguishbetweenpointtopointandbroadcast communicationmodes.Give one example
of each.
3. Explain the following terms.
a) Ground waves b) Space waves and c) sky waves.
4. What doesthe termLOS communicationmean?Name the types of waves that are used for
this communication. Give typical examples, with the help of a suitable figure, of
communication systems that use space wave mode propagation.
5. Write the function of 1) Transducer and 2) repeater in the context of communication
system.
6. What is modulation? Explain the need of modulating a low frequency information signal.
7. We do not choose to transmit an audio signal by just directly converting it to an E.Mwave
of the same frequency. Give two reasons for the same.

8. Explain briefly with the help of diagrams the terms (i) amplitude modulation and (ii)
Frequencymodulation.Whichof these (i) givesbetterqualitytransmission? (ii) Has a larger
coverage
9. Why is short wave bands used for long distance transmission of signals?
10. Optical and radio telescope are built on the ground but x-ray astronomy is possible only
from satellite?
11. Draw a block diagram for a transmitter and a receiver of AMwave.
3 MARKS
12. Define the termmodulationindexforanAMwave.What wouldbe the modulationindex for
an AMwave for which the maximum amplitude is ‘a’ and the minimum amplitude is b’
13. A TV tower has a height ‘h’. Derive an expression for maximum distance up to which the
signal can be received from the earth.
14. What ismeant by the term modulation? Explain with the help of a block diagram, how the
process of modulation is carried out in AMbroadcasts?
15. What is meantby‘production’of a modulated carrier wave? Describe briefly the essential
steps with block diagram production.
16. What is meant by ‘detection’ of a modulated carrier wave? Describe briefly the essential
steps with block diagram detection.

Kendriya Vidyalaya Sangathan, Silchar Region
Sample paper-1
Class XII- Physics
General Instructions
a. All questionsarecompulsory
b. Internalchoices havebeen provided in somequestions.You haveto attend only one
of the choices in such question.
c. Question numbers1 to 8 are very shortanswerquestionscarrying onemarkeach.
d. Question numbers9 to 18 are shortanswerquestionscarrying two markseach.
e. Question numbers19 to 27 are also very shortanswersquestionscarrying threemark
each.
f. Question numbers28 to 30 are long answertypequestion carrying 5 markseach
g. Uselog tables if necessary.
1. In which orientation, a dipole placed in uniform field is in (i) Stable (ii) Unstable
equilibrium? 1
2. Two different wires X and Y of same diameter but different materials are joined in
series across a battery. If the number density of electrons in X is twice that in ‘Y’ .
Find the ratio of drift velocity of electrons in two wires. 1
3. What is the magnetic moment of an electron orbiting in a circular orbit of radius ‘r’
with a speed ‘V’? 1
4. Name the part of electro magnetic spectrum whose wavelength lies in the range of
10 -10m . Give one of its use. 1
5. Red light is incident on a converging lens of focal length ‘f’ . State with reason how ‘f’
will change if red light is replaced by blue light. 1
6. How does the resolving power of telescope change when the aperture of the
objective is increased? 1
7. The stopping potential in an experiment on photo electric effect is 1.5V . What is the
maximum kinetic energy of the photoelectrons emitted? 1
8. Two nuclei have mass numbers in the ratio 1:8 , what is the ratio of their nuclei
radii? 1
9. Define electric flux. Write its SI unit. A charge q is enclosed by a spherical surface of
radius R. If the radius is reduced to half, how would the electric flux through the
surface change? 2
10. A infinite thin plane sheet of charge density 10 -8 cm -2 is held in air . How far apart
are two equipotential surfaces , whose potential difference is 5volt. 2
11. Give the expression for current sensitivity and voltage sensitivity of galvanometer.
Increase in current sensitivity may not necessarily increase the voltage sensitivity of
galvanometer. Justify. 2
12. An electric lamp having coil of negligible inductance connected in series with a
capacitor and an a.c source is glowing with certain brightness. How does the brightness
of the lamp change on reducing (i) capacitance (ii) frequency? 2

13. Find the wavelength of electromagnetic wave of frequency 4x10 9 Hz in free space .
Give its two applications. 2
14. For the same angle of incidence , the angle of refraction in media P, Q and R are 350 ,
250 and 150 respectively. In which medium will the velocity of light be maximum . Why?
2
15. Name one device for producing polarized light. Draw a graph showing the
dependence of intensity of transmitted light on the angle between polarizer and
analyser. 2
16. The radioactive nucleus ‘A’ undergoes a series of decays according to the following
scheme:
A α A1 β A2 α A3 ɣ A4 2
The mass number and atomic number of A are 180 and 72 respectivily. What are these
numbers for A4.
[OR]
Define activity of radio nuclei, write the S.I. unit . Give the plot of activity of a radio
active species versus time.
17. In a common emitter transmitter amplifier the d.c current gain β= 65, output
resistance is 5000 Ω and internal resistance of the transistor is 500Ω . Find the a.c
voltage gain and power gain. 2
18. What is the range of frequencies used in satellite communication? What is common
between these waves and light waves? 2
19. With a neat diagram, deduce the effect of introducing a dielectric slab in between
the plates of a parallel plates capacitor on the capacitance of a capacitor. 3
20. With the help of circuit diagram, describe a method to find the internal resistance of
a primary cell using potentiometer. 3
21. Four identical cells each of emf 2V, are joined in parallel providing supply of current
to external circuit consisting of two 15 Ω resistors joined in parallel. The terminal
voltage of the cells as read by an ideal Voltmeter is 1.6V. Calculate the internal
resistance of each cell. 3
22. Define self inductance and hence prove that the self inductance of a long air cored
solenoid is
L = (µ0 N2A)/ l 3
23. What is the effect on the interference fringes in a Youngs double slit experiment due
to each of the following operations. Explain with reason
(a). the separation between two slits is increased.
(b). the monochromatic source is replaced by another source of smaller wavelength.
(c). the source slit is moved closer to the double slit plane. 3

24. A proton and an alpha particle are accelerated through the same potential which
one of the two has (i) greater value of de-Broglie wavelength associated with it . (ii) less
kinetic energy? Justify your answer. 3
25. (a). Give the relation between decay constant and half life of a radio active element.
(b). A radio active substance has a half life period of 30days.Calculate (i) time takes for
¾ of original number of atoms to disintegrate. (ii) time taken for
1
8
of the original
number of atoms to remain unchanged.
[OR]
Calculate the longest and shortest wavelength in the Balmer series of hydrogen atom.
3
26. Why is modulation required in a transmitter? An audio signal of amplitude 0.1v is
used in amplitude modulation of a carrier wave of amplitude 0.2V. Calculate the
modulation index. 3
27. Your mother complaints of acute shortage of LPG. You are going to school without
having break-fast and without lunch box.
(a) Suggest a possible remedy to cook food in time
(b) What is the principle of such a device? 3
28. (a). Draw a schematic sketch of a cyclotron. Explain briefly how it works and how it
is used to accelerate the charged particles.
(b). Show that the time period of ions in cyclotron is independent of both speed and
radius of circular path.
(c) What is resonance condition? How is it used to accelerate the charged particles?
[OR]
(a) Distinguish between the magnetic properties of dia, para and ferro magnetic
substances in terms of (i) Susceptibility (ii) Magnetic permeability (iii) effect of
temperature.
(b) Draw the field lines due to external magnetic field near a (i) dia magnetic
(ii) para magnetic substance. 5
29. Trace the rays of light showing the formation of an image due to a point object
placed on the axis of a spherical surface separating the two media of refractive indices
n1 and n2 . (a) Establish the relation between the distance of object image and radius of
curvature from the central point of the spherical surface. (b). Hence derive the
expression for the lens makers formula.
[OR]

(a) State the condition under which the phenomenon of diffraction of light takes
place. Derive an expression for the width of central maxima due to diffraction of
light at single slit.
(b) A slit of width ‘a’ is illuminated by a monochromatic light of wave length 700nm
at normal incidence. Calculate the value of ‘a’ for
(i) first minima at an angle of diffraction of 300
(ii) at first maxima at an angle of diffraction of 300 5
30. Explain the working of a common emitter npn transistor amplifier with the help of a
neat circuit diagram. Hence give the expression for the (i) current gain (ii) Voltage gain
(iii) Power gain. 5
[OR]
Draw the output wave form at X, using the given inputs A and B for the logic circuit
shown. Also identify the logic operations performed by this circuit. Express the output
in the truth table for every combination of the given inputs.
------------------------------------------------------

Kendriya Vidyalaya Sangathan, Silchar Region
Sample Paper
Class XII- Physics
General Instructions
h. All questionsarecompulsory
i. Internalchoices havebeen provided in somequestions.You haveto attend only one
of the choices in such question.
j. Question numbers1 to 8 are very shortanswerquestions carrying onemarkeach.
k. Question numbers9 to 18 are shortanswerquestionscarrying two markseach.
l. Question numbers19 to 27 are also very shortanswersquestionscarrying threemark
each.
m. Question numbers28 to 30 are long answertypequestion carrying 5 markseach
n. Uselog tables if necessary.
1 Mark Questions
1 What is the value of A+B if A=1 and B=0 is Boolean Algebra?
2 Pieces of Cu & Ge are cooled from room temperature to 80 K. What will be the effect
on their resistance?
3 Blue light ejects electrons from photosensitive surface while orange light cannot. Will
violet & red light eject electrons from same surface?
4 Why does a convex lens of glass refractive index=1.5 behaves as a diverging lens when
immersed in Carbon di sulphide of refractive index=1.65?
5 Which types of em waves are used for cellular phones?
6 The electric current passing through a wire in the direction from Q to P is decreasing.
What is the direction of induced current in the metallic loop kept above the wire as
shown in fig?
7 An ammeter and mill ammeter are converted from the same Galvanometer, out of
two, which should have higher resistance?
8 Draw a graph of electric field  (r) with distance r from the centre of shell for 0≤r.
2 Mark Questions
9 Two dielectric slabs of dielectric constant k1 and k2 have been put in between the
plates of capacitor. Find the equivalent capacitor.
10 The following graph shows the variation of terminal potential V access a combination
of three cells in series to a resistor, versus current I , when will the dissipation of the
circuit be max?

11 State Kirchhoff rule. Use there rules to determine currents 1 2& 3
12 A particle of mass m and charge q moves at right angles to a uniform magnetic field.
Plot a graph showing the variation of radius of circular path described by it with the
increase in its (a) charge (b) kE where in each case other factors remain constant.
Justify your answer.
13 A metallic rod of length l is rotated at a constant angular speed  , normal to uniform
magnetic field B. Derive an expression for current induced if the resistance of rod is R.
14 A coil is connected to low voltage Bulb B and placed near another coil P as shown in
Fig. Give reason to explain the following observation:
a) The Bulb B lights
b) Bulbs get dimmer if the coil Q is moved towards left.
15 Two slits are made 1mm apart and the screen is placed 1m away. What is the fringe
width when blue green light of  500 nm is used?
What should be the width of each slit in order to obtain 10 maximum of the double slit
pattern within the central maximum of single slit pattern?
16 A plane em wave of frequency 25 MHz travels in free space along X- direction. At a
particular point in space & time. E=6.3j V/m. What is B at this point?
17 A TV tower has a height of 100m. How much population is covered by TV broadcast if
the Average population density near TV tower is 1500 km-2. (Re=6.37 * 106m).
18 Explain the formulation of depletion layer & potential barrier in p-n junction.
If the Input wave form is converted by a device X. Name the device and draw circuit
design.
3 Marks questions
19 How long can an electric lamp 100W be kept glowing by fusion of 2 kg of deuterium?

The fusion reaction H2
1 + H2
1 He3
2 + n1
0 + 3.27 Mev.
Or
Find the Q factor and KE of α-particle in α decay of Ra 226
88 .
(m Ra 226
88
= 22.6.0254 u
M α = 4.00260 u
Rn222
86
=222.01750 u )
20 An explosion occurred on August 6, 1945 when USA dropped an atom bomb on
Hiroshima, in Japan. This resulted in the killing of 66000 persons and injury 69000
persons. About 67% of the city structures smashed. Another nuclear accident occurred
in 1986 in USSR resulting in huge devastation. People living in that locality till today
suffer from genetic disorders due to gene mutation.
a) Name the nuclear reaction involved in the above case.
b) What consequences do the people living in such areas face?
c) As a responsible citizen, suggest a possible peaceful method to use the nuclear
energy.
21 What is momentum, speed and de-Broglie wavelength for an electron having Kinetic
Energy 120 eV.
22 What is the principle of Zener diode? How is it symbolically represented? With the
help of circuit diagram explain how Zener diode behaves like a Voltage stabilizer.
23 Explain with the help of block diagram explain the detection of an amplitude
modulated wave.
24 Draw a labelled ray diagram to show the formation of an image by compound
microscope. Write the expression for magnifying power. How does the resolving
power of compound microscope change when refractive index of the medium is
increased.
25 A series LCR circuit with L=0.12 H , C=480 nF , R=23 ohms is connected to 230V variable
frequency supply.
a) What is the source frequency for which the current amplitude is maximum?
b) What is the source frequency for which the average power absorbed by circuit
is maximum and obtain the value of this maximum power?
c) What is Q-factor?
26 State Huygene’s Principle. Using this principle prove Snell’s Law
27 A potential V is applied to a conductor of length L and diameter D, how are the electric
field and drift velocity affected
a) When voltage is doubled
b) When length is doubled
c) Diameter is doubled
5 Marks
28 Derive an expression for the intensity at any point on the observation screen in the
Young’s Double Slit experiment. Hence write the conditions for constructive and
destructive interference pattern
Or
Draw a graph to show the variation on (i-d) for prism. Deduce  =
)
2
sin(
)
2
sin(
A
dmA 
. A

monochromatic beam of light incident at an angle of 400 on prism suffers minimum
deviation if the angle of prism is 600, find the angle of minimum deviation.
29 Deduce an expression for Electric potential due to an electric dipole at any point on its
axis. Mention one contrasting feature of electric potential of a dipole at a point as
compared to that due to single change
Or
Write the principle of working of Van de Graaff generator. With the help of labelled
diagram describe its construction and working. How is the leakage of charge minimised
from the generator.
30 For a circular coil of radius R and N turns carrying current I , deduce the magnitude of
magnetic field at a point on its axis at a distance n from its centre.
B= 2/322
2
0
)(2 xR
NIR


a) What will be the magnetic field at the centre of the coil?
b) Consider two parallel coaxial coil of equal radius R and number of turns N, carry
equal currents I in the same direction separated by a distance R. show that
the field on the axis around the mid-point between the coils is given by
B=0.72
R
NI0
Or
A100 turn closely wound circular coil of radius 10 c.m. carries a current of 3.2 A.
a) What is the field at the centre of the coil?
b) What is the magnetic moment of this arrangement?
A coil is placed in a vertical plane and free to rotate about a horizontal axis which
coincides with its diameter. A uniform magnetic field of 2 tesla in the horizontal
direction exists such that initially the axis of the coil is in the same direction of the
field. The coil rotates through an angle of 900 under the influence of magnetic field
i) What are the magnitudes of torques on the coil in the initial and final
position?
ii) What angular speed is acquired by the coil when it is rotated by 900?
The moment of inertia of the coil is 0.1kgm2.

KENDRIYA VIDYALAYA SANGATHAN, SILCHAR REGION
2013-14

Sample Paper No.2 Class XII Subject : PHYSICS(Theory)

VALUE BASED QUESTIONS
1. Two personsare standingunderatree and anotherpersonnear them is inside a car. They were
arguingaboutgoingout for a movie orto the beach,when,alightningstruckthe tree withsome
force. The person inside the car notices his friends standing under the tree are affected by
lightning; he comes out and takes them to the nearby hospital.
a) Why the personinthe car wasnot affectedbylightning?Whatqualitydoyoufindin
the person inside the car?
b) Explain the process that takes place during lightning.
Ans: a) due to electrostatic shielding the person in the car was not affected (electric field
inside the metallicbodyiszero);helpingothers;takingaquickdecisionas to what is
to be done,incase,he isunaware or unable to do on his own. B) Refer NCERT Text
Book)
2. Duringan endoscopicsurgery,asurgeon sees the interior of the patient’s body on the viewing
screen of a video monitor. The surgeon continues to do the surgery with the help of other
medical staff and one of the medical staff on noticing the surgeon’s gloved fingers coming
withinafewcentimetersof ascreen,pointingtoa particularpart of the image,say,inexplaining
a surgical concernto othermedical staff,the gloves is contaminated. When one of the medical
staff asks the surgeon that whether his gloves would have been contaminated, the surgeon,
answers him later, after the completion of the operation.
a) What is learnt from the above?
b) Can you find the bacterial source? If yes, name it. AND
c) Name the force which plays a role in bacterial contamination.
(ANS: concentration & involvement in the work by the doctor, reply by the doctor-
answeringthe query without forgetting, observation of the medical attendant; b) yes,
charge; & c) electrostatic force)
3. ‘A’& ‘B’ are twostudentsina classwho have beenassignedtoorganize aRepublicDayfunction.
Theyhave alsobeeninstructedtoinvite personally more than 60 members from all the nearby
cultural organizations and VIPs in their area. While student ‘A’ arranged invitations using a
photocopier/fax, student ‘B’ arranges invitations by writing to them individually.
a) Which student’s method would you adopt and why? AND
b) State the principle behind the source used by student ‘A’.
(ANS: Student A because, he is aware of the latest technology and its applications; b)
electrostatic force
4. Fatherand a son returnedhome completelydrencheddue toheavyrain. Fatheradvisedhis son
not touch any electrical units with wet hands for he may get a shock; In spite of this, on
immediatelyenteringthe house,the sonswitchesonthe light(supplyvoltage is 220 V) and gets
a severe shock; He was fortunate notto getelectrocuted. Father, who is a Biologist, told that
when the skin is dry, resistance of a human body is 105
Ω; and when the skin is wet the body
resistance is 1500 Ω.
a) What is the lesson learnt by you?
b) Calculate the current that flow thro’ (I) a wet body and (ii) a dry body. AND
c) Dry skin or wet skin? - When will we have serious consequences and why?
(Ans: to obey elders; b) Using, I = V/R (i) 147 mA; (ii) 2.2 mA.; c) wet skin – with
147mA, when the current flows, the result is fatal)

5. Based on the previous knowledge learnt in the class,two students of class XII( A and B) were
askedto conductan experimentinthe laboratoryusingameterbridge-oneismade of Nichrome
and the otherone is made of Copper, of same length and same diameter of constant potential
difference. The student A could not give explanation for not achieving the result whereas
student B, could get the result and was also able to explain.
a) What made student B to perform successfully?
b) Give the formula to calculate the rate of heat production.
(ANS: a) student B had concentrated in the class room teaching and also had studied
again to remember what was taught; b) Refer NCERT Text book)
6. An oldwomanwhohad sufferedfromaheart stroke was taken to the hospital by her grandson
who is in class XII. The grandson has studied in Physics that, to save a person who is suffering
froma heartstroke,regularbeatingof the heartisto be restoredbydeliveringajoltto the heart
using a defibrillator, whose capacity is 70 microfarad and charged to a potential of 5000V and
energy stored in 875J; 200J of energy is passed thro’ a person’s body in a pulse lasting 2
milliseconds. The old woman gets panicked and refuses to be treated by defibrillator. Her
grandsonthenexplainstoherthe processthat would be adopted by medical staff and how the
result of that would bring her back to normalcy. The woman was then treated and was back to
normal
a) What according to you, are the values displayed by the grandson?
b) How muchpowerisdeliveredtothe bodyto save a person’s life from heart attack?
(ANS: Presence of mind, Knowledge of subject, Concern for his grandmother,
Empathy, Helping and caring; b) Power = energy / time; = 200/2 x 10-3
= 100KW)
7. Isabella used an induction stove and explains to her neighbor that due to shortage of LPG one
must utilize other sources that are available to produce heat energy; being a Physics teacher
Isabella,explains thatthe Oil companiesare trying their best to meet the demands for LPG and
that as a good citizenone mustuse othersourceswhereverfeasible. Isabella uses an induction
stove havinga value of 7H inductorand the flow of current is from 10Ato 7A in 9 x 10-2
seconds.
a) In the above, what is the quality you find in the Physics teacher?
b) Calculate the emf generated in the above?
(ANS:concern forthe nation,costeconomicattitude,sharingknowledge, & b) e =
-L dI / dt, = 233.3V)
8. A woman and her daughter of class XII in KV were in the kitchen, preparing a feast for visitors
usingthe newmicrowave ovenpurchased last evening. Suddenly, the daughter noticed sparks
inside the oven and unplugs the connection after switching it off. She found that inside the
microwave ovenametalliccontainerhadbeenkepttocookvegetable. She informs her mother
that no metallicobjectmustbe usedwhile cookinginmicrowave ovenandexplains the reasons
for the same.
a) What attitude of the daughter inspires you?
b) Give another use of a microwave oven
c) The frequency of microwave is 3 x 1011
Hz. Calculate its wavelength.
(ANS: Presence of mind, Knowledge of subject; b) used in telecommunication; & c) λ=
/c = (3 x 1011)
)/ (3 x 108
). = 10-3
.
9. Gopal visitshisfriendNaresh.Inhishouse Nareshwas playing with his kid sister and in spite of
the broad day light,Gopal noticesthe tube lightburning and advises him to save electricity; He
also claims that the heat inside the room increases which would lead to global warming.

a) What are the values associated with the decision saving electricity?
b) Whichelectromagneticwave isresponsible forincrease inthe average temperature
of the earth? Give other applications of the electromagnetic wave.
(ANS: a) concern for society/nation, awareness about global warming, b)
infrared waves; applications- to treat muscular strain, solar water heaters &
cookers)
10.Imran onenteringthe airportwasaskedto remove the contentsfromhispantand shirtpockets;
his hand bags and luggage were also checked by airport authorities by using a metal detector.
Imran gotannoyedand argued with the airport authority as to the reasons for such procedure.
The authoritytellshimthatall the passengersand their belongings will be checked for security
check to ensure safe travel.
a) What is the value that imparts us in the above scenario.
b) Briefly explain the working principle of a metal detector.
(ANS: a) respectinglawandobeyingthe rulesenactedbythe nation;self discipline andavoiding
arguments,b) change inthe magneticfieldina metal detector due to the metals carried by the
contents of checking which, induces change in current in the coil of the metal detector. This
detection of change sets up an alarm)
11.My friend and I have been assigned a work to choose a step down transformer for supply of
power for a small town with a demand of 1 MW at 220V situated 20km away from an electric
plant generates power at 440V; the resistance of the two line wires carrying power is
0.5ohm/km; two step down transformers are available- 4000V-220V & 100000V – 220V. Your
friend has chosen 100000V-220V step down transformer.
a) Asa studentof physics,whichstepdowntransformerwill youpreferforsupplyof apowerfor
a small town. Give reason.
b) What are the values associated with the above decision?
(ANS: a) I go withmy friends’ option, because Power loss is less in 100000V-220V that is why
Transmission of a.c over long distances is preferred for transmission.(hints: Iv=P/ Ev,
P=I2R,Power loss=output power/input power*100)b ) Knowledge is useful only when put to
practice and concern for country’s welfare.
12.During summer vacation Radha and Rani decided to go for a 3 D FILM. They have heard about
thisfilmthroughtheirfriends.Theywereaskedbuyspecialglassestoview the film.Before they
go for a movie, they approached their Physics teacher to know about these glasses. Physics
teacher explained when two polarizer’s are kept perpendicular to each other(crossed
polarizer’s) the lefteye seesonlythe image fromthe left end of the projector and the right eye
seesonlythe image fromthe rightlens.The twoimageshave the approximate perspectivesthat
the leftandright eyeswouldsee inrealitythe braincombine the imagestoproduce arealistic3-
D effect.
a) What qualities do these girls possess?
b) What do you mean by Polarization?
c) Mention the other applications of polarization.
(ANS: a) Curiosity to learn, approaching the teacher to learn new things, inquisitiveness
c) Refer NCERT text book) & c) Sun glasses, LCD,CD players)
13.Two students namely Ranjan and Praveen was asked to take up a project on efficient lighting
for road ways, cycle paths and bus lanes. They found LED IS THE BEST source for the above
said reasons. They collected the information from various sources and submitted the project
about its working, advantages and its applications by presenting with a good working model.

a) By seeing these two students, what kind of qualities you want adopt from them.
b) Explain LED with neat diagram and draw its symbol.
(ANS: a) Initiative, curiosity, punctuality, obedience & b) Refer NCERT text book)
14. Rahim, a class XI student of KV, visited his uncle and hears the burglar alarm on opening the
entrance door; his aunt welcomes him. He goes upstairs and asks his uncle who is a Physics
Lecturer, about the principle working of a burglar alarm. He discusses this with his class mates
and decides to present a program on ‘Burglar Alarm’ in the morning assembly.
a) How will you define the inquisitiveness of Rahim?
b) State the laws of photoelectric emission
(ANS: curiosity to learn, interest in the subject, sharing knowledge; b) Refer NCERT book)
15.I went out for shopping with my mother; during purchase of vegetables I noticed that the
Vendor used a digital weighing machine. On another shop, I noticed the vendor was using an
ordinary weighing machine. I remembered having studied about Logic Gates where, digital
codes are used.
a) What do you mean by Logic Gate? Mention the basic universal gates.
b) Draw symbols for OR, AND, & NOT
c) What is the value, in your opinion, that I created by the above incident.
(ANS: a) & b) – Refer NCERT Text book; c) concentration and observation in the class
room, retaining capacity, co-relating of what was taught with the real life incident)
16.Two persons were playing and one of them got injured as he fell from the top of a tree. He
was taken to the Hospital where, he was admitted for a fracture after X-ray. The boy’s
mother who on hearing the above incident rushed to the hospital, was worried and
restless; The other boy consoled her and the doctor who, overheard them, informed her
about the latest developments in the Medicine field and assured a speedy recovery of
her son.
a) How would you rate the qualities of the boy who consoled his friend’s mother?
b) How X-ray is produced?
c) Mention the fields where X-ray are used.
(ANS: caring for others, giving timely assistance, positive attitude; b) & c) Refer NCERT Text
book)
17. On our return from an excursion trip in our school, I noticed a bird sitting on a high voltage
electric wire. I curiously noticed the bird and found to my surprise that the bird flew off
after sometime without any electrical shock. This incident made me think of another incident
that took place near my house last week where, a boy, who climbed to take a kite, got severe
jolt of electric current. I immediately approached my school Physics teacher for an
explanation. My teacher explained the effect of electrical current which I told my mother that
evening.
a) What are the values associated with the above incident?
b) What would be the explanation given by the Physics teacher?
(ANS: a) observation, eagerness to learn; b) both the legs of the bird are at same voltage and
hence nocurrent passes;toreceive a shock there must be a potential difference between one
part of the body and another; if a person hangs from a high voltage wire without touching
anything else, he can be quite safe and would not feel shock)
18. Aathira and her father were hearing a running commentary of a test match played between
India and Srilanka in Mumbai from a radio set; suddenly the clarity of the sound decreased.
Beinga studentof physics,immediatelyAathiratunedthe receiverset and got the frequency of

the desiredsignal fromthe desiredstation.The amplitudeof the currentbecame highandit was
received in their set. Father was happy and was praised his daughter.
a) What made Aathira’s father to be proud of her?
b) Which determines the sharpness of the tuning at resonance and define the term
involved in it)
(ANS: a) presence of mind, application of knowledge; b) Q factor, for Definition-refer NCERT
text book)
19.Two students Ram and Anand were reading the newspaper. The Headlines in the news paper
was aboutthe nuclearpowerplantwhichwasto be set upat Kodangulam.This was objected to
by the local people. There was a healthy debate about nuclear power plant between Ram and
Anand.Ram was supporting the people who were objecting, saying that power plant will emit
harmful radiations and local people will be affected by it. Whereas Anand was against Ram’s
views.He mentionedthatgreat scientists, including our former President Dr. Abdulkalam, and
our Government had taken every care to provide safety measures with the best and latest
technology.
a) What do you think of the new Kodangulam power plant – a boon or a sin?
b) Define nuclear fission AND
c) What is the role of control rods in nuclear reactor?
(ANS:a) boon– powerplantwoulderadicate power shortage, and the Tamilnadu govt. can
also sell excess power to other states; b) & c) – Refer NCERT Text Book)
20.Ajay of class XII had a passion to become an Astronaut. He always spoke about the astronauts
and their life in the space with others. He was encouraged by his teachers, parents and his
friends. He completed XII with merit and became a scientist in ISRO. He got an opportunity to
workin NASA.One dayhisdreamcame intorealityashe was askedto fly to space with three of
his colleagues. In the space he experienced a state of weightlessness.
a) What made Ajay to fulfill his dream? AND
b) What do you mean by weightlessness?
(ANS:a) Determination,hardworking,curiosity;b) It is a situation in which the observed weight
of the body becomes zero)
21. Ashwini of class XI,used to come to school with her father by a two wheeler by crossing a
bridge.One dayshe foundthatthe bridge wascollapsed; causality was there. Her father had to
take her ona differentroute toreachthe school. Her mind was still preoccupied with what she
had seenatthe brokenbridge;she wasdisturbed.Onthe wayto school she asked herself many
questions about the collapse. On reaching school, she immediately approached her physics
teacher and narrated the incident. On hearing the reasons and explanations given by her
teacher she decided to pursue her carrier as a civil engineer and vowed to construct 100%
quality dams and bridges.
a) What qualities do you find in her?
b) Name the property that helps in constructing the bridges and also name the material to
be used?
(ANS: a) Sympathy, determination, & concern for the society; b) elasticity and the material
to be used is triangular shaped steel)
22. Aurag’smotheris sufferingfromDiabetesandalways worries about her disease. Anurag, who
is a doctor himself, treats his mother. He has used paper chromatography for conducting the
urine testto determinethe sugarlevel of hismotherandfindsthathismotherisnormal.Anurag
not only takes care of his mother but also takes interests in the welfare of other patients who
visit him. He vows to expertise in his field and decides to serve the poor.

a) What values do you find in Anurag?
b) Which phenomenon is found in paper chromatography? AND
C) Define the phenomenon.
(ANS: concern not only for his mother but also the poor and needy, knowledge, awareness
about latest technology; b) capillarity & c) ‘rise or fall of a liquid’ inside a tube of narrow
bore).
23.One day,there was paper news highlighting the good values of one of our school student. The
newswasabout an accident,where,tworiders of a motor bike had a head-on collision with an
upcomingbusand got thrownoff tothe pedestrianpavementatthe side. While, the rider, who
was wearinghelmet,gotawaywithminorinjury,the pillion rider was severely wounded as, he
was not wearing helmet. One of our school students who was nearby, got into the act of
assistingthe injuredandcalledthe ambulance andalsoinformed the police. The very next day,
thisact of our school studentwaspublishedbyone of the local newspaperandeventhe parents
of the wounded visited our school and thanked the student and also praised our school
management. The impact of collision of the student with helmet and the one without it were
discussed in one our physics class.
a) What does the above accident teach us?
b) Explain the above scenario in terms of impact AND
c) What values of the school student do you notice?
(ANS: a) the above accident tells us to use helmets irrespective of whether you are the rider
or you are a pillion rider; b) in terms of impact, the above scenario tells us that ‘force is
inversely proportional to time’, i.e., in the case of the person wearing helmet, the time
for impact is more, as against the time for the person without helmet; & c) Sympathy,
timely action - intimation to the right person/personnel at the right time)
24.Selvi, a student of class XI, came across her servant maid on way to her house after visiting a
friend.Selvinoticedthatthe servantmaidwas findingitdifficulttoread the bus number and on
nearingshe helpedhertogetinto the bus.. She enquired and found that the servant maid had
defectsinhereyesightandhaddifficultyinviewingfarawayobjectsandwas notin a positionto
afford for a check- up with an eye specialist. She immediately took her to a nearby
ophthalmologist. She arranged for eye check-up of her servant maid and paid the doctor’s fee
fromher pocketmoney/savingsandalsopurchasedhermedicinesprescribedbythe doctor. The
doctor after checking advised the servant maid to wear spectacles and gave her the power of
spectacles to be worn by her.
a) What values do you see in Selvi?
b) Explain the eye defect of the servant maid using Physics term and also give the
rectification to be adopted with ray diagram.
(ANS:helpingthe poorandneedy,takingpromptandtimelyaction;spending money for a good
deed; b) Refer NCERT Text book)
25.Arun and Naveen studying in KENDRIYA VIDYALAYA watched the film “Swadesh” together
getting inspiration from the film,they realized the need of the hour for the conservation of
energy. Together they decided to do something for the nation. With the help of their school
teachersandprincipal they arranged an exhibition to depict the various renewable sources of
energy and the applications of it.
a) What values must have highlighted so that the youngsters are motivated?
b) Explain the working of a solar cell with a neat diagram.
(ANS: a) Need to conserve energy with the motto of sustainable development in
fulfillingthe needsof the present generation without compromising the need of the

future generation,takinganinitiative,bringingawarenessamongthe studentsandthe
society) Refer NCERT text book) *************
List of reference books and websites- Physics Study Material
Reference Book
1. Conceptual Physics : Paul G Hewitt
2. Principles of Modern Physics : Arthur Beiser
3. University Physics : Young, Freedman : Addison-WeslyLongman,Inc
4. The Feynman Lectures on Physics: Feynman, Leighton& Sands : Narora Publishing
House, New Delhi.
5. Physics Vol I & II : Robert Resnick, David Halliday & Kenreth S Krane : Wiley India
6. Problems in General Physics : I E Irodov : Global Publications
7. Principles of Physics : Brij Lal & Subbramanyam : Eurasia Publication company
(Pvt.) Ltd, New Delhi
8. Schaum’s Solved Problems Series : Alvin Hulpern : McGraw hill Book Company,
New Delhi
9. Conceptual Physics : Paul G Hewitt : Addison – Wesley Publishing Company,
California
10. IIT Physics – Tata McGraw Hill

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Class XII Physics Study Material