Dtdm theory book soft copy 2

Electricity
From the word “Elektron”
Greek for “amber”
Electricity is simply the flow of
electrons.

“Laws of Attraction”
Opposite Charges Attract
Like Charges Repel
+ -
+ +

Coulombs Law
 The force between charges varies inversely
with the square of their separation
distances.
+ +
+ +

Static Electricity
 What can you rub together to make static electricity?
(Let’s list them.)
 When you rub a balloon on your hair you scrape
electrons off the atoms of your hair onto the balloon.
 The atoms of the balloon apparently have more “grab”
on electrons.

 Electric field is defined as being present in
any region where a charged object
experiences an electric force.
 Normally the charged object is taken as the
test charge
 The force that is felt is also dependent on
the amount of charge on the test charge
Electric Field

 Therefore Field Intensity or Field Strength
is described as the ratio of Force to the
amount of test charge.
 The field intensity for an electric field is
measured in Newtons per Coulomb [N/C].
 Field Intensity is a vector quantity
 The size of the vector is given by

 The electric field of a point charge can be
obtained from Coulomb's law:
The electric field is radially outward from the
point charge in all directions.
The circles represent spherical equipotential
surfaces.

The electric field from any number of point
charges can be obtained from a vector sum
of the individual fields.
A positive number is taken to be an outward
field; the field of a negative charge is toward
it.

 direction of the field is taken to be the
direction of the force it would exert on a
positive test charge.
 electric field is radially outward from a positive
charge and radially in toward a negative point
charge.

Electric Potential
 The electric potential of a point may also be
defined as the work done in carrying a unit
positive charge from infinity to that point.
 The electric potential at a point r in a static
electric field E is given by the line integral

Potential due to a Point Charge
 Consider two points 'a' and 'b' in an electrostatic field
of a single isolated point charge +q.
If a unit positive charge 'q' moves from 'a' to 'b' without
acceleration, then the potential difference between 'a'
and 'b' is given as

= - Edl
 But dl = - dr
[This is because when we move a distance 'dl' towards
the source, we move in the direction of decreasing of
'r']
From equation (1), we have

 If the point 'a' is at infinity, then
 From the above, it is evident that for a given charge 'q', potential
depends only on 'r'. Therefore, if the charge is positive, potential
is positive and if the charge is negative, potential is negative.

Electric Field Intensity due to Spherical
Shell
• Let σ be the uniform surface charge density of a thin
spherical shell of radius R.
• The field at any point P, outside or inside, can depend
only on r (the radial distance from the centre of the shell
to the point) and must be radial (i.e., along the radius
vector).
(i) Field outside the shell: Consider a point P outside the
shell with radius vector r.
To calculate E at P, we take the Gaussian surface to be a
sphere of radius r and with centre O, passing through P.
All points on this sphere are equivalent relative to the
given charged configuration.
The electric field at each point of the Gaussian surface,
therefore, has the same magnitude E and is along the
radius vector at each point.

Thus, E and ΔS at every point are parallel and the flux through
each element is E ΔS. Summing over all ΔS, the flux through the
Gaussian surface is E × 4 π r2. The charge enclosed is σ × 4 π R2.
By Gauss’s law
• The electric field is directed outward if q > 0 and inward if q
< 0. This, however, is exactly the field produced by a charge q
placed at the centre O. Thus for points outside the shell, the
field due to a uniformly charged shell is as if the entire charge of
the shell is concentrated at its centre.

(ii) Field inside the shell: In Fig., point P is inside the
shell. The Gaussian surface is again a sphere through P
centred at O.
The flux through the Gaussian surface, calculated as
before, is E × 4 π r2. However, in this case, the
Gaussian surface encloses no charge. Gauss’s law then
gives E × 4 π r2 = 0 i.e., E = 0 (r < R).

 The field due to a uniformly charged thin shell is zero
at all points inside the shell. This important result is a
direct consequence of Gauss’s law which follows from
Coulomb’s law.

 Stores electrical charges
 Does not consume any voltage
 Absorbs voltage changes – Spikes
 Discharges back into circuit
 Rated in farads and microfarads
Capacitance

Capacitors
insulator
conductor

Capacitance : Definition
 Take two chunks of conductor
 Separated by insulator
 Apply a potential V between
them
 Charge will appear on the
conductors, with Q+ = +CV on
the higher-potential and Q- = -
CV on the lower potential
conductor
 C depends upon both the
“geometry” and the nature of the
material that is the insulator
0
V
Q+ = +CV
+++++++++++
+++++++++++
+++++++++++
V

Parallel-Plate Capacitor
Area A -Q
e
dl
E
d
Area A
+Q
âz
Qd
V
A
e
 
  
 
Q A
C
V d
e
 

Capacitors in Parallel
 Three capacitors (C1,
C2, and C3) are
connected in parallel
to a battery B.
 All the capacitor plates
connected to the
positive battery
terminal are positive.
 All the capacitor plates
connected to the
negative battery
terminal are negative.

 When the capacitors are first connected in the circuit,
electrons are transferred through the battery from
the plate that becomes positively charged to the plate
that becomes negatively charged.
 The energy needed to do this comes from the battery.
 The flow of charge stops when the voltage across the
capacitor plates is equal to that of the battery.
 The capacitors reach their maximum charge when the
flow of charge stops.

 In the parallel circuit, the
voltage (joules/coulomb) is
constant.
Vab = V1 = V2 = V3
 The total charge stored on
the capacitor plates is equal
to the charge on each plate.
Q = Q1 + Q2 + Q3

 In order to make problem
solving easier, we replace the
three capacitors with a single
capacitor that has the same
effect on the circuit as the
three single capacitors.
 In parallel:
Ceq = C1 + C2 + C3 + ...

 Ceq will be equal to the total capacitance of
the circuit CT.
 Increasing the number of capacitors
increases the capacitance.

 Problem solving involves reducing the circuit
components to one total charge, one total voltage,
and one total capacitance:
 In parallel circuits, you will probably find the
voltage first and then use this to determine the
charge found on each capacitor.
V
Q
C T
T 
V
C
Q
V
C
Q 2
2
1
1 




Capacitors in Series
 Three capacitors (C1, C2, and C3)
are connected in series to a
battery B.
 When the capacitors are first
connected in the circuit,
electrons are transferred through
the battery from the plate of C1
that becomes positively charged
to the plate of C3 that becomes
negatively charged.

 As the negative charge increases on
the negatively charged plate of C3,
an equal amount of negative charge
is forced off the plate of C3 that
becomes positive onto the plate of C2
that becomes negative.
 The same amount of negative charge
is also moved between C2 and C1.
 The energy needed to do this comes
from the battery.

 In the figure shown, all of the
upper capacitor plates will have a
charge of +Q and all of the lower
capacitor plates will have a
charge of –Q.
 For capacitors in series, the
amount of charge on each plate is
the same:
QT = Q1 = Q2 = Q3 = ...

 In order to make problem solving
easier, we replace the three
capacitors with a single capacitor
that has the same effect on the
circuit as the three single
capacitors.
 In series, the reciprocal of the total
capacitance is the sum of the
reciprocals of the separate
capacitors:





3
2
1
eq C
1
C
1
C
1
C
1

 It is easier to use the reciprocal
key (x-1 or 1/x) on your
calculator:
Ceq = (C1
-1 + C2
-1 + C3
-1 + …)-1
 In series, the total voltage is
equal to the combined voltage of
each capacitor:
VT = V1 + V2 + V3 + ...

 Ceq will be equal to the total capacitance of
the circuit CT.
 Increasing the number of capacitors
decreases the capacitance.

 Problem solving involves reducing the circuit
components to one total charge, one total voltage,
and one total capacitance:
 In series circuits, you will probably find the charge
first and then use this to determine the voltage
across each capacitor.
V
Q
C T
T 
2
2
1
1
C
Q
V
C
Q
V 


Capacitors In Parallel and In
Series
 A circuit as shown on the left
when both S1 and S2 are
closed is actually 2 sets of
capacitors in parallel with
the 2 parallel combinations
arranged in series.

Capacitors In Parallel and In
Series
 The points c and d allows
charge to move between the
capacitors.
 C1 and C2 are in parallel with
each other.
 C3 and C4 are in parallel with
each other.
 The C12 parallel combination
and the C34 parallel
combination are in series with
each other.

ELECTRIC CURRENT
 Is the rate of electron flow
 Measure in amperes or amps
 As voltage goes up, current goes up
 As voltage goes down, current goes down

RESISTANCE
Opposition to current flow – measured
in ohms
Size, type, length, temperature and
physical condition of conductor affect
its resistance
An increase in resistance causes a
decrease in current flow.
Voltage drops as current flows through
resistance

VOLTAGE
 Electrical pressure or potential
 The Electromotive force that causes the movement
of electons
 Electrical pressure is measured in volts
 Automotive electrical systems run on 12 volts

POTENTIAL DROP
 Is the amount of electrical pressure lost or consumed
as it pushes current through a resistance
 The Sum (total) of all voltage drops in an electrical
circuit will always equal source voltage – all the voltage
is used up.

OHMS LAW
E = Voltage
I = Current flow
R = Resistance
E / I = R
E / R = I
I x R = E

E=12V R=12W I?
E=? R=120W I0.1A
E=12V R=24W I?
E=12V R=? I=24A

Specific Resistance
 specific resistance, or resistivity, is the resistance in
ohms offered by a unit volume (the circular-mil-
foot or the centimeter cube) of a substance to the
flow of electric current.
 Resistivity is the reciprocal ofconductivity.
 A substance that has a high resistivity will have a
low conductivity, and vice versa. Thus,the specific
resistance of a substance is the resistance of a unit
volume of that substance.

 Many tables of specific resistance are based on the
resistance in ohms of a volume of a substance 1foot
in length and 1 circular mil in cross-sectional area.
 The temperature at which the resistance
measurement is made is also specified.
 If you know the kind of metal a conductor is made
of, you can obtain the specific resistance of the
metal from a table. The specific resistances of some
common substances are given in table 1-1.

The resistance of a conductor
of a uniform cross section
varies directly as the
product of the length and the
specific resistance of the
conductor, and inversely as
the cross-sectional area of the
conductor.

Temperature Coefficient of
Resistance
 A temperature coefficient describes the relative
change of a physical property that is associated
with a given change in temperature For a
property R that changes by dR when the
temperature changes by dT, the temperature
coefficient α is defined by

 Here α has the dimension of an inverse
temperature and can be expressed e.g. in 1/K or K−1
 If the temperature coefficient itself doesn't vary too
much with temperature, a linear approximation
can be used to determine the value R of a property
at a temperature T, given its value R0 at a reference
temperature T0.

 The temperature dependence of electrical
resistance and thus of electronic devices (wires,
resistors) has to be taken into account when
constructing devices and circuits. The temperature
dependence of conductors is to a great degree
linear and can be described by the approximation
below.
Where

Positive temperature coefficient
of resistance
 A positive temperature coefficient (PTC)
refers to materials that experience an increase
in electrical resistance when their temperature
is raised. Materials which have useful
engineering applications usually show a
relatively rapid increase with temperature, i.e. a
higher coefficient. The higher the coefficient,
the greater an increase in electrical resistance
for a given temperature increase.

 Negative temperature coefficient of
resistance
 A negative temperature coefficient (NTC) refers to
materials that experience a decrease in electrical
resistance when their temperature is raised.
Materials which have useful engineering
applications usually show a relatively rapid
decrease with temperature, i.e. a lower coefficient.
The lower the coefficient, the greater a decrease in
electrical resistance for a given temperature
increase.

Types of effects
 Heating effect
 Chemical effect
 Magnetic effect
When an Electric current flow it produces
following type of Effects:-

Heating effect
 When current flows in a wire, the wire heats up.
 Joule studied this effect and found experimentally that
the amount of heat energy given out by a wire depends
on several factors.

W (heat energy )  I2
 R
 t (time)
THUS W  R I2t
W = k R I2 t
For SI units the constant k =1
W = R I2 t Watt
Joule’s Law

States that the rate at which heat produced in
a conductor is directly proportional to the
square of the current provided its resistance is
constant.
 So P = I 2R
Where,
 P = Power in Watt.
 I= Current in Ampere.
 R = Resistance in Ohm.
Joule’s Law

Joule’s Law
 Power = rate at which work is done.
= rate at which heat is produced. = W /t.
 Where W = Energy Produced
t = Time Period
P = R I2 Joule’s Law
The rate at which heat is produced in a conductor is
directly proportional to the square of the current
provided the resistance is constant P  I2

 Expression for Power Loss:
 Let 'q' amount of electric charge passes through a
conductor in unit time, the electric current
through the conductor is given by:
I = q/t
Or
q = I x t ............... (1)

During the flow of electric current energy lost in the
form of heat is equal to q x V, where V is the
potential difference across the ends of conductor.
 Energy lost = q x V
 Putting the value of q, we get
 Energy lost = I x t x V
Energy lost/t = VI
 But Energy /t = Power
 Power = VI

 POWER LOSS IN TERMS OF CURRENT AND
RESISTANCE
 According to Ohm's law V = IR. putting the value of
V, we get
 Power = (IR)I
Power = I2R

 POWER LOSS IN TERMS
OF RESISTANCE AND POTENTIAL
DIFFERENCE
 As power = VI and according to Ohm's law I = V/R, putting
the value of i, we get
 Power = VI
Power = V (V/R)
Power = V2/R

 UNIT OF POWER
 In SI system unit of power is Watt.
Other large units are:
1. Kilowatt KW (1000 watt)
2. Megawatt W(106 watt)
Energy and resistors
• In a resistor, we find that the charges move through a change
in potential. Therefore, there must be a change in the
potential energy of the electrons. However, we also know that
the current in a metal is constant for a constant potential
change and resistance. It is just given by:
 Therefore, the electrons move at a constant velocity and do
not increase their kinetic energy. Where does the potential
energy go? It goes into heat.

Series Circuits
 Two elements in a series
 Connected at a single point
 No other current-carrying connections at this point
 A series circuit is constructed by connecting various
elements in series

Resistors in series
1 2
eq
R R R
 
R2
R1
v2
v1
+ +
+
_
_
_
v i1
A B
C
I

Resistors in series
 Analogous formula is true for any number of resistors,
 It follows that the equivalent resistance of a series
combination of resistors is greater than any of the
individual resistors

Resistors in parallel
Since both R1 and R2 are connected to the same battery,
potential differences across R1 and R2 are the same,
1 2
1 1 1
eq
R R R
 
I
I2 I1
R2 R1
V
+
_
I
Req
V
+
_
or 1 2
1 2
eq
R R
R
R R



Resistors in parallel: notes
 Analogous formula is true for any number of resistors,
 It follows that the equivalent resistance of a parallel
combination of resistors is always less than any of the
individual resistors

• Electromagnetic induction is the production of
an electromotive force across a conductor when it
is exposed to a varying magnetic field.
• It is described mathematically by Faraday's law of
induction, named after Michael Faraday who is
generally credited with the discovery of induction
in 1831.
• Electromagnetic induction was discovered
independently by Michael Faraday in 1831 and
Joseph Henry in 1832.
Magnetic Induction

 Faradays Laws of electromagnetic Induction.
 In 1831, Micheal Faraday formulated two laws on the
bases of experiments. These laws are called Faraday's
laws of electromagnetic induction.
 FIRST LAW
 First Law of Faraday's Electromagnetic Induction state
that whenever a conductor are placed in a varying
magnetic field emf are induced which is called
induced emf, if the conductor circuit are closed
current are also induced which is called induced
current.
 Or
 Whenever a conductor is rotated in magnetic field emf
is induced which are induced emf.

SECOND LAW
 Second Law of Faraday's Electromagnetic Induction
state that the induced emf is equal to the rate of
change of flux linkages (flux linkages is the product of
turns, n of the coil and the flux associated with it).

Self Induction and Mutual Induction
 Self Induction
 When a time-dependent i.e. a varying current flows
through a coil, the flux through the coil )due to the
magnetic field produced by current in it) will keep on
changing. Hence an induced e.m.f. will be produced in
it. This process is called self induction.
 For any given coil it is found that
 where L is constant for the given coil.

 The quantity L depends on the geometry of the coil
and is called Coefficient of Self Inductance.
 S.I Unit of L = 1 Volt / 1 Amp / sec = 1 Henry
 Note : 1 Volt / Amp = 1 Ohm
 1 Henry = 1 Ohm *sec

Mutual Induction
 If two coils are kept close to each other and if a varying current
flows through one of them then the intensity of the magnetic field
intensity () due to the current will vary.
 Hence flux through the other coil will keep on changing with time;
therefore an e. m. f. will be induced in the other coil. For any given
combination of coils it is found that
 where M is constant and is called the Coefficient of Mutual
Inductance of the given arrangement of the given coils.
 The quantity M, like L, also depends on the geometry of coils and
their arrangements.
 S.I Unit of M = 1 henry.

EMF Produced by a Changing Magnetic Field
 A loop of wire is connected to a sensitive ammeter.
 When a magnet is moved toward the loop, the ammeter
deflects.
 The direction was chosen to be toward the right.
Faraday’s Laws of Electromagnetic Induction

EMF Produced by a Changing Magnetic
Field
 When the magnet is held stationary, there is
no deflection of the ammeter
 Therefore, there is no induced current
 Even though the magnet is in the loop

EMF Produced by a Changing Magnetic
Field
 The magnet is moved away from the loop.
 The ammeter deflects in the opposite direction.

Summary
 The ammeter deflects when the magnet is moving
toward or away from the loop.
 The ammeter also deflects when the loop is moved
toward or away from the magnet.
 Therefore, the loop detects that the magnet is
moving relative to it.
 We relate this detection to a change in the magnetic
field.
 This is the induced current that is produced by an
induced emf.

Faraday’s Experiment
 A primary coil is connected to a switch and a battery.
 The wire is wrapped around an iron ring.
 A secondary coil is also wrapped around the iron ring.
 There is no battery present in the secondary coil.
 The secondary coil is not directly connected to the primary
coil.

Faraday’s Experiment – Results
 At the instant the switch is closed, the
galvanometer (ammeter) needle deflects in
one direction and then returns to zero.
 When the switch is opened, the
galvanometer needle deflects in the
opposite direction and then returns to zero.
 The galvanometer reads zero when there is a
steady current or when there is no current in
the primary circuit.

Faraday’s Experiment – Conclusions
 An electric current can be induced in a circuit by
a changing magnetic field.
 This would be the current in the secondary
circuit of this experimental set-up.
 The induced current exists only for a short time
while the magnetic field is changing.
 This is generally expressed as: an induced emf is
produced in the secondary circuit by the
changing magnetic field in the primary.
 The actual existence of the magnetic flux is not
sufficient to produce the induced emf, the flux
must be changing

Faraday’s Law – Statements
 Faraday’s law of induction states that “the emf
induced in a circuit is directly proportional to the
time rate of change of the magnetic flux through the
circuit”
 Mathematically,
B
d
ε
dt

 

Faraday’s Law – Statements, continued
 If the circuit consists of N loops, all of the same
area, and if FB is the flux through one loop, an
emf is induced in every loop and Faraday’s law
becomes:-
B
d
ε N
dt

 

Factors affecting an EMF
The magnitude of B can change with
time.
The area enclosed by the loop can
change with time.
The angle q between B and the normal
to the loop can change with time.
Any combination of the above can occur.

Lenz’s Law, (Minus Sign in Faraday)
 Lenz’s law: the induced current in a loop is in
the direction that creates a magnetic field
that opposes the change in magnetic flux
through the area enclosed by the loop.
 The induced current tends to keep the
original magnetic flux through the circuit
from changing.
 Examples :-
 Jumping Ring; Tube & Magnet

SELF INDUCTANCE
AND
MUTUAL INDUCTANCE
Effects of induced EMF

Self-inductance
 Self-inductance occurs when the changing flux
through a circuit arises from the circuit itself.
 As the current increases, the magnetic flux through
a loop due to this current also increases.
 The increasing flux induces an emf that opposes
the change in magnetic flux.
 As the magnitude of the current increases, the rate
of increase lessens and the induced emf decreases.
 This opposing emf results in a gradual increase of
the current.

Self-inductance cont
• The self-induced emf must be proportional to the
time rate of change of the current.
• L is a proportionality constant called the
inductance of the device.
• The negative sign indicates that a changing current
induces an emf in opposition to that change.
I
L
t
e

 


Self-inductance, final
 The inductance of a coil depends on geometric
factors.
 The SI unit of self-inductance is the Henry.
 1 H = 1 (V · s) / A.
 You can determine an expression for L.
B B
N
L N
I I
 
 


 The machines those are involve with D.C
,these machines are known as D.C
Machines.
 D.C Machines are of two types
 D.C Motors
 D.C Generators

D.C GENERATORS
 Generator is a electromechanical energy
conversion device which converts
Mechanical Energy into Electrical Energy
Principle of Generator
• When flux linked with the coil changes then
an e m f is induced in the coil.
• Whenever a coil is rotated in a magnetic
field an e.m.f. will be induced in this coil.

 Circuit Diagrams of Various Generators
 Separately excited D.C Generator
Self excited D.C generator
D.C shunt generator

 D.C Series Generator
 D.C Compound wound Generator
 Short Shunt Generator

 D.C Motors
Motor is a electromechanical energy conversion device
which converts electrical energy into mechanical
energy.
Principle of operation of motor
Whenever a current coil is placed under a magnetic
field the coil experiences a mechanical force, and is
given by
F= BIlSinθ Newtons/coil side.
Where, I is the current through the coil in ampere.
The direction of the force acting is fixed by applying
the Fleming’s left hand rule.

Circuit diagram of Various types D.C motor
Permanent Magnet D.C Motor
Separately excited D.C Motor

 Self excited D.C motor
 D.C shunt Motor
 D.C Series Motor

 D.C Compound wound Motor
 Long Shunt D.C Motor
Short Shunt D.C Motor

Emf equation of Generator
 D.C Generator E.M.F Equation, Terminal Voltage and
Ratings
 E.M.F Equation
Let
Φ = flux/pole in weber
Z = total number of armeture conductors
= No. of slots x No. of conductors/slot
P = No. of generator poles
A = No. of parallel paths in armature
N = armature rotation in revolutions per minute
(r.p.m)
E = e.m.f induced in any parallel path in armature
Generated e.m.f Eg = e.m.f generated in any one of
the parallel paths i.e E.

• Average e.m.f geneated /conductor
= dΦ/dt volt (n=1)
• Now, flux cut/conductor in one revolution dΦ
= ΦP Wb
• No. of revolutions/second = N/60
• Time for one revolution, dt = 60/N second
• Hence, according to Faraday's Laws of
Electromagnetic Induction,
E.M.F generated/conductor is


 For a simplex wave-wound generator
No. of parallel paths = 2
No. of conductors (in series) in one path =
Z/2
E.M.F. generated/path is

 For a simplex lap-wound generator
No. of parallel paths = P
No. of conductors (in series) in one path = Z/P
E.M.F .generated/path
 In general generated e.m.f
 where A = 2 - for simplex wave-winding
= P - for simplex lap-winding

An alternating function or AC
Waveform is defined as one that varies in
both magnitude and direction in more or
less an even manner with respect to time
making it a “Bi-directional” waveform.
An AC function can represent either a
power source or a signal source with the
shape of an AC waveform generally
following that of a mathematical sinusoid
as defined by:-A(t) = Amax x sin(2πƒt).

 The term AC or to give it its full description
of Alternating Current generally refers to a
time-varying waveform with the most
common of all being called
a Sinusoid better known as a Sinusoidal
Waveform.
 Sinusoidal waveforms are more generally
called by their short description as Sine
Waves. Sine waves are by far one of the most
important types of AC waveform used in
electrical engineering.

 AC Waveform Characteristics
 The Period, (T) is the length of time in seconds that
the waveform takes to repeat itself from start to finish.
This can also be called the Periodic Time of the
waveform for sine waves, or thePulse Width for square
waves.
 The Frequency, (ƒ) is the number of times the
waveform repeats itself within a one second time
period. Frequency is the reciprocal of the time period,
( ƒ = 1/T ) with the unit of frequency being the Hertz,
(Hz).
 The Amplitude (A) is the magnitude or intensity of
the signal waveform measured in volts or amps.

 Relationship Between Frequency and Periodic Time
Average Value of an AC Waveform
 For a pure sinusoidal waveform this average or mean
value will always be equal to 0.637 x Vmax and this
relationship also holds true for average values of
current.

The RMS Value of an AC Waveform
 The effective or RMS value of an alternating current is measured in
terms of the direct current value that produces the same heating effect
in the same value resistance. The RMS value for any AC waveform can
be found from the following modified average value formula.
 RMS Value of an AC Waveform
Where: n equals the number of mid-ordinates.
 For a pure sinusoidal waveform this effective or R.M.S. value will always
be equal to 1/√2 x Vmax which is equal to 0.707 x Vmax and this
relationship holds true for RMS values of current. The RMS value for a
sinusoidal waveform is always greater than the average value except for
a rectangular waveform. In this case the heating effect remains
constant so the average and the RMS values will be the same.

Form Factor and Crest Factor
 Although little used these days, both Form
Factor and Crest Factor can be used to give
information about the actual shape of the AC
waveform. Form Factor is the ratio between the
average value and the RMS value and is given as.
 For a pure sinusoidal waveform the Form Factor
will always be equal to 1.11. Crest Factor is the ratio
between the R.M.S. value and the Peak value of the
waveform and is given as.

 For a pure sinusoidal waveform the Crest Factor will
always be equal to 1.414.
Capacitive Reactance
 As the capacitor charges or discharges, a current flows
through it which is restricted by the internal resistance
of the capacitor. This internal resistance is commonly
known as Capacitive Reactance and is given the
symbol XC in Ohms.

Capacitive Reactance has the electrical symbol “Xc” and has
units measured in Ohms the same as resistance, ( R ). It is
calculated using the following formula:
 Where:
 Xc = Capacitive Reactance in Ohms, (Ω)
 π (pi) = 3.142 (decimal) or 22÷7 (fraction)
 ƒ = Frequency in Hertz, (Hz)
 C = Capacitance in Farads, (F)

 Impedance, denoted Z, is an expression of the
opposition that an electronic component, circuit, or
system offers to alternating and/or dielectric current .
 Impedance is a vector (two-dimensional)quantity
consisting of two independent scalar (one-
dimensional)phenomena: resistance and reactance .

 From the above triangle we get
 Inductance-
In electromagnetism and electronics, inductance is the
property of a conductor by which a change in current
flowing through it "induces" (creates) a voltage
(electromotive force) in both the conductor itself (self-
inductance) and in any nearby conductors
(mutual inductance).

 Like resistance, reactance is measured in Ohm’s
but is given the symbol “X” to distinguish it from a
purely resistive “R” value and as the component in
question is an inductor, the reactance of an
inductor is called Inductive Reactance, ( XL ) and
is measured in Ohms.
 Its value can be found from the formula.

RLC Circuit
 An RLC circuit (the letters R, L and C can be in other
orders) is an electrical circuit consisting of a resistor,
an inductor, and a capacitor, connected in series or in
parallel. The RLC part of the name is due to those
letters being the usual electrical symbols for resistance
inductance and capacitance respectively.
 Series RLC Circuit

 Individual Voltage Vectors
 Phrasor Diagram

 Voltage triangle for a series R.L.C Circuit
 We know that

 By substituting these values into Pythagoras’s equation
above for the voltage triangle will give us

Filter Introduction
 Basically, an electrical filter is a circuit that can be
designed to modify, reshape or reject all unwanted
frequencies of an electrical signal and accept or pass
only those signals wanted by the circuits designer. In
other words they “filter-out” unwanted signals and an
ideal filter will separate and pass sinusoidal input
signals based upon their frequency.
 In low frequency applications (up to 100kHz), passive
filters are generally constructed using
simpleRC (Resistor-Capacitor) networks, while higher
frequency filters (above 100kHz) are usually made
from RLC (Resistor-Inductor-Capacitor) components.

 Filters are so named according to the frequency range
of signals that they allow to pass through them, while
blocking or “attenuating” the rest. The most
commonly used filter designs are the:
 1.The Low Pass Filter – the low pass filter only allows
low frequency signals from 0Hz to its cut-off
frequency, ƒc point to pass while blocking those any
higher.

 2. The High Pass Filter – the high pass filter only allows
high frequency signals from its cut-off
frequency, ƒc point and higher to infinity to pass
through while blocking those any lower.

 3. The Band Pass Filter – the band pass filter allows
signals falling within a certain frequency band setup
between two points to pass through while blocking
both the lower and higher frequencies either side of
this frequency band.

 Simple First-order passive filters (1st order) can be
made by connecting together a single resistor and a
single capacitor in series across an input signal,
( Vin ) with the output of the filter, ( Vout ) taken
from the junction of these two components.
 Depending on which way around we connect the
resistor and the capacitor with regards to the
output signal determines the type of filter
construction resulting in either a Low Pass Filter
or a High Pass Filter.

 Machines those work in alternating current
are known as A.C Machines
 Like D.C Machines A.C Machines are of two
types
 1.A.C Generators(Alternators)
 2.A.C Motors

A.C Generators or Alternators
 It generates the electrical power in the form
alternating voltage and current.
 Alternate always rotate in synchro nous
speed. Therefore its other name is
synchronous generator
 Synchnous speed is defined as
Ns=120f/P
Where Ns-Synchronous speed
f- 50Hz
P- no. of poles

 Different types of alternators
 According to application alternators are classified
as-
 Automotive type - used in modern automobile.
 Diesel electric locomotive type - used in diesel
electric multiple unit.
 Marine type - used in marine.
 Brush less type - used in electrical
power generation plant as main source of power.
 Radio alternators - used for low brand radio
frequency transmission.

 According to the rotor construction alternators are
divided into two types
 1.Cylindrical type
 2.Salient Pole type
 The alternator has two parts
 Stator
 Rotor
 Stator-
The stator frame is used to hold the armature
windings in alternators, and in case of larger
diameter alternators (which are slow speed) the
stator frame is cast out of sections and there are
holes for ventilation in the casting itself.

Rotor-
Salient Pole type Rotor

 Smooth Cylindrical Pole type Rotor

 Difference between salient Pole type and cylindrical
Pole type

 For the generation of electricity we require
a D.C generator which is also known as
Exciter
 The exciter is connected to the rotor part of
the alternator
 As the rotor rotates the field related to the
stator winding changes and emf is induced
in the stator winding
 At the power plants the voltage that is
generated is generally 11KV.

 AC Motors
Generally AC motor are of two type s
1.Synchronous Motors
2.Induction Motors
Among these two motors induction motors are generally
used
Induction Motors
An induction motor always runs at a speed less than
synchronous speed because the rotating magnetic
field which is produced in the stator will generate flux in
the rotor which will make the rotor to rotate, but due to the
lagging of flux current in the rotor with flux current in the
stator, the rotor will never reach to its rotating magnetic
field speed i.e. the synchronous speed.

 Two types of induction motors are there
 Single phase Induction motor
 Three Phase induction motor
Single Phase Induction Motor
Induction motor runs on single Phase
Types of Single Phase Induction Motor
Split phase induction motor
Capacitor start induction motor
Capacitor start capacitor run induction motor
Shaded pole induction motor

 Some Diagrams of single Phase induction Motor

Three Phase induction Motor
 Three phase induction motor are of two types
 Squirrel cage induction motor
 Slip ring induction motor
 Squirrel cage Induction Motor

 Slip ring Induction Motor
 Advantage of 3 phase induction motor over
synchronous motor-
 Induction motors are singly excited and synchronous
motors are doubly excited
 To start single/three phase induction motor we require
single/three phase supply but for starting synchronous
motor we required both A.C and D.C sypply

Transformer
 Transformer is static device which transfers power
from one winding to another winding with increase in
voltage and correspondingly decrease in current and
vice versa with constant frequency.
 Types of transformer
1. Power transformer
2. Auto Transformer
3. Current transformer
4. Potential Transformer
5. Booster Transformer
6. Audio Frequency Transformer
7. Radio Frequency Transformer

Transformer work on the principleof Faraday’s Laws of
electromagnetic induction
Equation of transformer
Let's say, T is number of turns in a winding,
 Φm is the maximum flux in the core in Wb.
 As per Faraday's law of electromagnetic induction

Where φ is the instantaneous alternating flux and
represented as,
As the maximum value of cos2πft is 1, the maximum value of
induced emf e is,
To obtain the rms value of induced counter emf, divide this
maximum value of e by √2.

 This is EMF equation of transformer.
 If E1 & E2 are primary and secondary emfs and T1 &
T2 are primary and secondary turns then,voltage
ratio or turns ratio of transformer is,

Various types of transformer
Power Transformer
Current Transformer

 Potential Transformer
 Auto Transformer

 Booster Transformer
Audio Frequency Transformer

 Radio Frequency Transformer

Dielectric
 A dielectricmaterial (dielectric for short) is an
electrical insulator that can be polarized by an
applied electric field.
When a dielectric is placed in an electric field, electric
charges do not flow through the material as they do in
a conductor, but only slightly shift from their average
equilibrium positions causing dielectric
polarization.
 Every insulator can be forced to conduct electricity.
This phenomena is known as dielectric breakdown.

Atomic Dipole
 A non-degenerate (S-state) atom can have only a
zero permanent dipole. This fact follows quantum
mechanically from the inversion symmetry of
atoms. All 3 components of the dipole operator are
antisymmetric under inversion with respect to the
nucleus,
 where is the dipole operator and is the
inversion operator.

Dipole Moment
 Dipole moment can be defined as the product of
magnitude of charges and the distance of separation
between the charges.

Dipole Interaction
 Dipole-Dipole interactions result when two polar
molecules approach each other in space. When this
occurs, the partially negative portion of one of the
polar molecules is attracted to the partially positive
portion of the second polar molecule. This type of
interaction between molecules accounts for many
physically and biologically significant phenomena
such as the elevated boiling point of water.

 A liquid dielectric is a dielectric material in liquid state. Its
main purpose is to prevent or rapidly quench electric
discharges.
 Dielectric liquids are used as electrical insulators inhigh
voltage applications, e.g. transformers, capacitors, high
voltage cables, and switchgear (namely high voltage
switchgear). Its function is to provide electrical insulation,
suppress corona and arcing, and to serve as a coolant.
 A good liquid dielectric should have high dielectric strength,
high thermal stability and chemical inertness against the
construction materials used, non-flammability and low
toxicity, good heat transfer properties, and low cost.
 Liquid dielectrics are self-healing; when an electric
breakdown occurs, the discharge channel does not leave a
permanent conductive trace in the fluid.
Dielectric Liquids

Semiconductor materials
 A semiconductor is a substance whose resistivity is
less than that of an insulator but more than that of a
conductor.
 Some commonly used semiconductor materials are
germanium and silicon.
 Intrinsic Semiconductor
 A semiconductor in an extremely pure form is known
as an intrinsic semiconductor.

Extrinsic Semiconductor
 The instrinsic semiconductor has little conductivity
at room tempreture.
 Its conductivity can be increased by the addition of a
small amount of suitable metallic impurity. It is then
called impurity or extrinsic semiconductor.

Extrinsic Semiconductors are classified
in to P-type and N-type semiconductor
 P-type: A P-type material is one in
which holes are majority carriers i.e.
they are positively charged materials
(++++)
N-type: A N-type material is one in
which electrons are majority charge
carriers i.e. they are negatively charged
materials (-----)

Diodes
Electronic devices created by bringing together a p-
type and n-type region within the same semiconductor
lattice. Used for rectifiers, LED etc

It is represented by the following symbol, where the
arrow indicates the direction of positive current flow.

Forward Bias and Reverse Bias
 Forward Bias : Connect positive of the Diode to
positive of supply…negative of Diode to negative of
supply
 Reverse Bias: Connect positive of the Diode to negative
of supply…negative of diode to positive of supply.

Characteristics of Diode
 Diode always conducts in one direction.
 Diodes always conduct current when “Forward Biased”
( Zero resistance)
 Diodes do not conduct when Reverse Biased
(Infinite resistance)

I-V characteristics of Ideal diode

I-V Characteristics of Practical Diode

Shockley Equation















 1
exp
T
D
s
D
nV
v
I
i
q
kT
VT 
Is is the saturation current ~10 -14
Vd is the diode voltage
n – emission coefficient (varies from 1 - 2 )
k = 1.38 × 10–23 J/K is Boltzmann’s constant
q = 1.60 × 10–19 C is the electrical charge of an
electron.
At a temperature of 300 K, we have
mV
26

T
V

Rectification
 A rectifier is an electrical device that
converts alternating current (AC), which
periodically reverses direction, to direct
current (DC), which is in only one direction, a
process known as rectification.

Types of Rectifiers
 Rectifier are of two types
1.Half wave rectifier
2.Full wave rectifier
Full wave reactifier is of two types
 1.Center tap reactifer
 2.Bridge reactifer

Half wave rectifier
 In half wave rectification, either the positive or
negative half of the AC wave is passed, while the
other half is blocked.
 Because only one half of the input waveform
reaches the output, it is very inefficient if used for
power transfer.

Half wave rectifier working animation
The Below diagram shows the flow of electrons

Half wave rectification
The wave form after the half wave rectification

full wave rectifier
 A full-wave rectifier converts the whole of the input
waveform to one of constant polarity (positive or negative)
at its output.
 Full-wave rectification converts both polarities of the input
waveform to DC (direct current), and is more efficient.

Full wave Center Tap reactifier
Circuit

DC Output Voltage
Root Mean Square (RMS) Value of Output Voltage

Output voltage of the full wave rectifier Animation

Bridge rectifier
 A bridge rectifier makes use of four diodes in a
bridge arrangement to achieve full-wave
rectification.

Bridge reactifier circuit with
waveform

A transistor is a device that can be used as either an
amplifier or a switch. Let’s first consider its operation
in a simpler view as a current controlling device.
Transistor

Basic Transistor Operation
Look at this one circuit as two separate circuits, the base-emitter(left
side) circuit and the collector-emitter(right side) circuit. Note that the
emitter leg serves as a conductor for both circuits.
The amount of current flow in the base-emitter circuit controls the
amount of current that flows in the collector circuit. Small changes in
base-emitter current yields a large change in collector-current.

Transistor Structure
With diodes there is one p-n junction. With
bipolar junction transistors (BJT), there are
three layers and two p-n junctions. Transistors
can be either pnp or npn type.

Transistor Characteristics and
Parameters
As previously discussed,
base-emitter current
changes yield large
changes in collector-
emitter current. The factor
of this change is called
beta().
 = IC/IB

Parameters
There are three key dc voltages and three key dc currents to be
considered. Note that these measurements are important for
troubleshooting.
IB: dc base current
IE: dc emitter current
IC: dc collector current
VBE: dc voltage across
base-emitter junction
VCB: dc voltage across
collector-base junction
VCE: dc voltage from
collector to emitter

Transistors Characteristics and
Parameters
For proper operation, the base-emitter junction is
forward-biased by VBB and conducts just like a diode.
The collector-base junction is reverse biased by VCC
and blocks current flow through it’s junction just like a
diode.
Remember that
current flow
through the base-
emitter junction will
help establish the
path for current
flow from the
collector to emitter.

Parameters
Analysis of this transistor circuit to predict the dc voltages and
currents requires use of Ohm’s law, Kirchhoff’s voltage law and
the beta for the transistor.
Application of these laws begins with the base circuit to determine
the amount of base current. Using Kirchhoff’s voltage law, subtract
the .7 VBE and the remaining voltage is dropped across RB.
Determining the current for the base with this information is a
matter of applying of Ohm’s law. VRB/RB = IB
The collector current is
determined by
multiplying the base
current by beta.
.7 VBE will be used in most analysis examples.

Parameters
What we ultimately
determine by use of
Kirchhoff’s voltage law for
series circuits is that in the
base circuit VBB is
distributed across the
base-emitter junction and
RB in the base circuit. In
the collector circuit we
determine that VCC is
distributed proportionally
across RC and the
transistor(VCE).

Parameters
E
C
C
I
I /
D


Collector characteristic
curves give a graphical
illustration of the relationship of
collector current and VCE with
specified amounts of base
current. With greater increases
of VCC , VCE continues to
increase until it reaches
breakdown, but the current
remains about the same in the
linear region from .7V to the
breakdown voltage.

Parameters
With no IB the transistor is in the cutoff region and
just as the name implies there is practically no
current flow in the collector part of the circuit. With
the transistor in a cutoff state the the full VCC can
be measured across the collector and emitter(VCE)

Parameters
Current flow in the collector part of the circuit is,
as stated previously, determined by IB multiplied
by . However, there is a limit to how much
current can flow in the collector circuit regardless
of additional increases in IB.

Parameters
Once this maximum is reached, the transistor is said
to be in saturation. Note that saturation can be
determined by application of Ohm’s law.
IC(sat)=VCC/RC The measured voltage across the now
“shorted” collector and emitter is 0V. (Example 4-4)

Parameters
The dc load line graphically illustrates IC(sat) and cutoff
for a transistor.

Parameters
CE
D
C V
P /
I (max)

The beta for a transistor is not always constant.
Temperature and collector current both affect beta,
not to mention the normal inconsistencies during the
manufacture of the transistor.
There are also maximum power ratings to consider.
The data sheet provides information on these
characteristics.

Transistor Amplifier
Amplification of a relatively small ac voltage can be had
by placing the ac signal source in the base circuit.
Recall that small changes in the base current circuit
causes large changes in collector current circuit.
The small ac voltage causes the base current to increase
and decrease accordingly and with this small change in
current the collector current will mimic the input only with
greater amplitude.

Transistor as Switch
A transistor when used as a switch is simply being
biased so that it is in cutoff (switched off) or saturation
(switched on). Remember that the VCE in cutoff is VCC
and 0 V in saturation.

Current Gain of transistor
Transistors are used to amplify current and so in
an examination you could be asked to find the
BASE current or COLLECTOR current or the
GAIN. The GAIN is simply the amount of
amplification.

Integrated Circuit
•An integrated circuit or monolithic integrated circuit (also
referred to as an IC, a chip, or a microchip) is a set
of electronic circuits on one small plate ("chip")
of semiconductor material, normally silicon.
•This can be made much smaller than a discrete
circuit made from independent components. ICs can be
made very compact, having up to several
billion transistors and other electronic components in an
area the size of a fingernail

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