Ekeeda - First Year Enginering - Basic Electrical Engineering

EKEEDA – FIRST YEAR ENGINEERING
BASIC ELECTRICAL ENGINEERING
II B. Tech I semester

UNIT-I
Introduction to Electrical Engineering

Ohms Law: At constant temperature potential difference across the conductor is directly proportional to
current flowing through the conductor is called ohms law.
V ∝I
V=IR
wherethe constant of proportionality Ris calledtheresistance or electricalresistance, measured in
ohms (Ω). Graphically, the V − Irelationship for a resistor according to Ohm‟slaw is depicted in
Figure
Figure V −Irelationshipfor aresistor accordingto Ohm‟slaw.
At any given point in the above graph, the ratio of voltage to current is always constant
basic circuit components:

Circuit Element Voltage Current
Resistor
Inductor
Capacitor
V = IR
v = L
di
dt
v = 1
¸ t
idt + v(0) C
0
I =
V
R
i = 1
¸ t
dt
v
L 0
i = C
dv
, i = 0 for DC
dt
V − I relationships for a resistor, inductor and capacitor.
Kirchhoff’s Voltage Law (KVL)
Kirchhoff‟s Voltage Law states that the algebraic sum of voltages around each loop at any instant of time is
zero
Σ voltage drops = Σ voltage rises
Kirchhoff’s Current Law (KCL)
Kirchhoff‟s Current Law states that The algebraic sum of currents a node at any instant is zero. Σ
currents in = Σ currents out
Basic Definitions:
Current: the directed flow of electrons (charge) called current. It is denoted by I. units are Amps
Electrical potential: charged body capacity to do work is known as its electrical potential.
Potential difference: difference in potentials of two charged bodies is called Potential difference
Power: the rate at which an electrical work done in electrical work is called power. It is denoted by P. units are
Watt
Electrical work: Electrical work is said to be done when there is transfer of charge. It is denoted by W. units
are joules.
Energy: capacity to do work is called energy.
Electrical Network: A combination of various electric elements (Resistor, Inductor, Capacitor, Voltage source,
Current source) connected in any manner what so ever is called an electrical network
Classification of element:
We may classify circuit elements in two categories, passive and active elements.
Passive Element: The element which receives energy (or absorbs energy) and then either converts it into heat
(R) or stored it in an electric (C) or magnetic (L) field is called passive element.

Active Element: The elements that supply energy to the circuit is called active element. Examples of active
elements include voltage and current sources, generators
Bilateral Element: Conduction of current in both directions in an element (example: Resistance; Inductance;
Capacitance) with same magnitude is termed as bilateral element
Unilateral Element: Conduction of current in one direction is termed as unilateral (example: Diode,
Transistor) element
Linear Circuit: Roughly speaking, a linear circuit is one whose parameters do not change with voltage or
current. More specifically, a linear system is one that satisfies (i) homogeneity property (ii) additive property
Non-Linear Circuit: Roughly speaking, a non-linear system is that whose parameters change with voltage or
current. More specifically, non-linear circuit does not obey the homogeneity and additive properties.
DC Sources
In general, there are two main types of DC sources
1. Independent (Voltage and Current) Sources
2. Dependent (Voltage and Current) Sources
An independent source produces its own voltage and current through some chemical reaction and
does not depend on any other voltage or current variable in the circuit. The output of a dependent
source, on the other hand, is subject to a certain parameter (voltage or current) change in a circuit
element. Herein, the discussion shall be confined to independent sources only.
DC Voltage Source
This can be further subcategorised into ideal and non-ideal sources.
The Ideal Voltage Source An ideal voltage source, shown in Figure has a terminal voltage which is
independent of the variations in load. In other words, for an ideal voltage source, the supply
current alters with changes in load but the terminal voltage, VL always remains constant. This
characteristic is depicted in Figure .
(a) An ideal voltage source. (b) V − I characteristics of an ideal voltage
source.
Figure: Schematic and characteristics of an ideal voltage source
Practical Voltage Source For a practical source, the terminal voltage falls off with an increase in
load current. This can be shown graphically in Figure. This behavior can be modeled by assigning
an internal resistance, Rs, in series with the source as shown in Figure

Where RL represents the load resistance. The characteristic equation of the practical
voltage source can be written as
VL = Vs − RsI
For an ideal source, Rs = 0 and therefore VL = Vs.
Resistive Circuits
Series Resistors
Parallel Resistors
Series Inductors
Parallel Inductors

Series Capacitors
Parallel Capacitors
Delta – Star Conversion

Star -Delta Conversion
Superposition Theorem
Superposition theorem is extremely useful for analysing electric circuits that contains two or more active
sources. In such cases, the theorem considers each source separately to evaluate the current through or voltage
across a component. The resultant is given by the algebraic sum of all currents or voltages caused by each source
acting independently. Superposition theorem can be formally stated asfollows
“The current through or voltage across any element in a linear circuit containing several sources
is the algebraic sum of the currents or voltages due to each source acting alone, all other sources
being removed at thattime.”
Linearity is a necessary condition for the theorem to apply. Fortunately, the v, i relationship for R, and C
are all linear.The sources can be removed using the following methodology
1. Ideal voltage sources are short-circuited
2. Ideal current sources are open-circuited
In general, practical sources are replaced by their internal resistances.
Thévenin’s Theorem
Thévenin‟s theorem provides a useful tool when solving complex and large electric circuits by reducing them to a
single voltage source in series with a resistor. It is particularly advantageous where a single resistor or load in a
circuit is subject to change.
Formally, the Thévenin‟s theorem can be stated as
“Any two-terminal linear electric circuit consisting of resistors and sources, can be replaced
by an equivalent circuit containing a single voltage source in series with a resistor connected
across the load.”
In the circuit diagrams shown in Figure, the current IL through the load resistance RL is the same. Hence the
circuits are equivalent as far as the load resistor RL is concerned.

4Rs
Pmax = Vs2
Figure : Illustration of Thévenin‟s theorem.
The following steps outline the procedure to simplify an electric circuit using Thévenin‟s theorem where VT H
and RT H are the Thévenin‟s voltage and Theévenin‟s resistance respectively.
1. Remove the load resistance RL.
2. VT H is the open circuit (OC) voltage across the load terminalsand
3. RT H is the resistance across the load terminals with all sources replaced by their internal resistances.
Alternatively, measure the OC voltage across, and the short circuit (SC) current through the load terminals.
Then
VT H = Voc and RT= Voc/ Isc
Maximum Power Transfer Theorem
As discussed in the section on Thévenin‟s theorem, any DC network of sources and resistances can be replaced
by a single voltage source in series with a resistance connected across the load (see Figure). The maximum
power transfer theorem states that the power delivered to the load is maximum when the load resistance, RL
is equal to the internal (source) resistance, Rs of the DC power supply. In other words, it can be said that the
load resistance must match the Thévenin‟s resistance for maximum power transfer to take place i.e.,
(Rs = RT H ) = RL
When this occurs, the voltage across the load resistance will be Vs and the power delivered to the load
is given by 2
The above equation is plotted in Figure which clearly demonstrates maximum power delivered when Rs = RL.
Under this condition, the maximum power will be
0
R ()
R = R
P
max
PL
(W)

Figure: Illustration of maximum power transfer theore

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UNIT-II
Alternating Quantities

Principle of AC voltage: Consider a rectangular coil of N turns placed in a uniform magnetic field as shown in
the figure. The coil is rotating in the anticlockwise direction at an uniform angular velocity of ω rad/sec
When the coil is in the vertical position, the flux linking the coil is zero because the plane of the coil is parallel
to the direction of the magnetic field. Hence at this position, the emf induced in the coil is zero. When the coil
moves by some angle in the anticlockwise direction, there is a rate of change of flux linking the coil and
hence an emf is induced in the coil. When the coil reaches the horizontal position, the flux linking the coil is
maximum, and hence the emf induced is also maximum. When the coil further moves in the anticlockwise
direction, the emf induced in the coil reduces. Next when the coil comes to the vertical position, the emf
induced becomes zero. After that the same cycle repeats and the emf is induced in the opposite direction.
When the coil completes one complete revolution, one cycle of AC voltage is generated. The generation of
sinusoidal AC
Voltage can also be explained using mathematical equations. Consider a rectangular coil of N turns placed in a
uniform magnetic field in the position shown in the figure. The maximum flux linking the coil is in the
downward direction as shown in the figure. This flux can be divided into two components, one component
acting along the plane of the coil Φmaxsinωt and another component acting perpendicular to the plane of the coil
Φmaxcosωt.
ω rad/sec

θ
Фmaxsinωt
Фmax
Фmaxcosωt
The component of flux acting along the plane of the coil does not induce any flux in the coil. Only the
component acting perpendicular to the plane of the coil ie Φmaxcosωt induces an emf in the coil.
Angular Frequency (ω)
Angular frequency is defined as the number of radians covered in one second(ie the angle covered by the
rotating coil). The unit of angular frequency is rad/sec.
Advantages of AC system over DC system
1. AC voltages can be efficiently stepped up/down using transformer
2. AC motors are cheaper and simpler in construction than DCmotors
3. Switchgear for AC system is simpler than DC system
Definition of Alternating Quantity
e
+Em
0
-EmT
π/2 π 3π/2 2π ωt

An alternating quantity changes continuously in magnitude and alternates in direction at regular intervals of time.
Important terms associated with an alternating quantity are defined below.
Amplitude
It is the maximum value attained by an alternating quantity. Also called as maximum or peak value
Time Period (T)
It is the Time Taken in seconds to complete one cycle of an alternating quantity
Instantaneous Value
It is the value of the quantity at any instant
Frequency (f)
It is the number of cycles that occur in one second. The unit for frequency is Hz or cycles/sec. The
relationship between frequency and time period can be derived as follows.
Time taken to complete f cycles = 1 second Time taken
to complete 1 cycle = 1/f second
T = 1/f
Average Value
The arithmetic average of all the values of an alternating quantity over one cycle is called its average value
Average value = Area under one cycle
Base
For Symmetrical waveforms, the average value calculated over one cycle becomes equal to zero because the
positive area cancels the negative area. Hence for symmetrical waveforms, the average value is calculated for half
cycle.
Average value = Area under one half cycle
Base

RMS or Effective Value
The effective or RMS value of an alternating quantity is that steady current (dc) which when flowing through a
given resistance for a given time produces the same amount of heat produced by the alternating current
flowing through the same resistance for the same time.
Form Factor
The ratio of RMS value to the average value of an alternating quantity is known as Form
Factor
Peak Factor or Crest Factor
The ratio of maximum value to the RMS value of an alternating quantity is known as
the peak factor
Phasor Representation

An alternating quantity can be represented using
(i) Waveform
(ii) Equations
(iii) Phasor
A sinusoidal alternating quantity can be represented by a rotating line called a Phasor. A phasor is a line of
definite length rotating in anticlockwise direction at a constant angular velocity
The waveform and equation representation of an alternating current is as shown. This sinusoidal quantity
can also be represented using phasors.
i
+Im
0
-Im i = Im sin t
π 2π ωt

Draw a line OP of length equal to Im. This line OP rotates in the anticlockwise
direction with a uniform angular velocity ω rad/sec and follows the circular trajectory
shown in figure. At any instant, the projection of OP on the y-axis is given by
OM=OPsinθ = Imsinωt. Hence the line OP is the phasor representation of the
sinusoidal current

Phase
Phase is defined as the fractional part of time period or cycle through which the
quantity has advanced from the selected zero position of reference
Phase of +Em is π/2 rad or T/4
sec Phase of -Em is 3π/2 rad or
3T/4 sec
Phase Difference
When two alternating quantities of the same frequency have different zero points,

they are said to have a phase difference. The angle between the zero points is the
angle of phase difference.
In Phase
Two waveforms are said to be in phase, when the phase difference between them is
zero. That is the zero points of both the waveforms are same. The waveform, phasor
and equation representation of two sinusoidal quantities which are in phase is as
shown. The figure shows that the voltage and current are in phase.
Lagging
In the figure shown, the zero point of the current waveform is after the zero point
of the voltage waveform. Hence the current is lagging behind the voltage. The
waveform, phasor and equation representation is as shown.
Leading
In the figure shown, the zero point of the current waveform is before the zero point of

the voltage waveform. Hence the current is leading the voltage. The waveform,
phasor and equation representation is as shown.

=
m
AC circuit with a pure resistance
Consider an AC circuit with a pure resistance R as shown in the figure. The alternating
voltage v is
given
by
v V
sint
m
---------- (1)
The current flowing in the circuit is i. The voltage across the resistor is given as VR
which is the same asv.
Using ohms law, we can write the following relations
i = I sin t
--------------- (2)
Wher
e
Vm
Im =
R
From equation (1) and (2) we conclude that in a pure resistive circuit, the voltage and
current are in phase. Hence the voltage and current waveforms and phasors can be

drawn as below.

m
AC circuit with a pure inductance
Consider an AC circuit with a pure inductance L as shown in the figure. The alternating
voltage v is
given
by
v =Vm
sint
---------- (1)
The current flowing in the circuit is i. The voltage across the inductor is given as VL
which is the same asv.
i = I sin(t −  / 2) ------------------- (2)
From equation (1)
and (2) we observe
that in a pure
inductive circuit, the
current lags behind
the voltage by 90⁰.
Hence the voltage
and current
waveforms and
phasors can be
drawn as below.
The inductive reactance XL is given as

=
L= 2fL
AC circuit with a pure capacitance
Consider an AC circuit with a pure capacitance C as shown in the figure. The alternating
voltage v is
given
by
V sint
m
---------- (1)
The current flowing inthe
circuit.
i = Im sin(t + / 2) -------------------(2)
From equation (1) and (2) we observe that in a pure capacitive circuit, the current leads
the voltage by 90⁰. Hence the voltage and current waveforms and phasors can be
drawn as below.

Capacitive reactance
The capacitive reactance XC is given as
X =
1
L
C
Vm
=
1
2fC
Im =
XC
It is equivalent to resistance in a resistive circuit. The unit is ohms (Ω)
R-L Series circuit
Consider an AC circuit with a resistance R and an inductance L connected in series as
shown in the figure. The alternating voltage v is given by
v = V
m
sint
The current flowing in the circuit is i. The voltage across the resistor is VR and that across
the inductor is VL.
VR=IR is in phase with I
VL=IXL leads current by 90 degrees
With the above information, the phasor diagram can be drawn as shown.

The current I is taken as the reference phasor. The voltage VR is in phase with I and
thevoltageVLleadsthecurrentby90⁰.TheresultantvoltageVcanbedrawnasshowninthe figure.
FromthephasordiagramweobservethatthevoltageleadsthecurrentbyanangleΦorinother wordsthe current
lagsbehindthevoltagebyanangleΦ.

L
The waveform and equations for an RL series circuit can be drawn as below.
V = Vm sin t
I = Im sin(t −)
From the phasor diagram, the expressions for the resultant voltage V and the angle Φ
can be derived asfollows.
V =
VR = IR
VL = IX L
V =
V = I
V = IZ
R2
+ X2
Where impedance Z
The impedance in an AC circuit is similar to a resistance in a DC circuit. The unit for
impedance is ohms(Ω).
V 2
+ V2
R L
(IR)2
+ (IX L )
2
=R2
+ X 2
L

Impedance Triangle
We can derive a triangle called the impedance triangle from the phasor diagram of
an RL series circuit as shown
The impedance triangle is right angled triangle with R and XL as two sides and
impedance as the hypotenuse. The angle between the base and hypotenuse is Φ.
Power
In an AC circuit, the various powers can be classified as
1. Real or Active power
2. Reactive power
3. Apparent power
Real or active power in an AC circuit is the power that does useful work in the
cicuit. Reactive power flows in an AC circuit but does not do any useful work. Apparent
power is the total power in an AC circuit.

From the phasor diagram of an RL series circuit, the current can be divided into two
components. One component along the voltage IcosΦ, that is called as the active
component of current and another component perpendicular to the voltage IsinΦ that
is called as the reactive component of current.
Real Power
The power due to the active component of current is called as the active power or real
power. It is denoted by P.
P = V x ICosΦ = I2
R
Real power is the power that does useful power. It is the power that is consumed by the
resistance. The unit for real power in Watt(W).
Reactive Power
The power due to the reactive component of current is called as the reactive power. It is
denoted by Q.
Q = V x ISinΦ = I2
XL
Reactive power does not do any useful work. It is the circulating power in th L and C
components.The unit for reactive power is Volt Amperes Reactive (VAR).
Apparent Power
The apparent power is the total power in the circuit. It is denoted by S.
S = V x I = I2
Z
S =
The unit for apparent power is Volt Amperes (VA).
Power Triangle
From the impedance triangle, another triangle called the power triangle can be derived
as shown.
P2
+ Q2

The power triangle is right angled triangle with P and Q as two sides and S as the
hypotenuse. The angle between the base and hypotenuse is Φ. The power triangle
enables us to calculate the following things.
1. Apparent power S =
Cos =
P
= Re alPower
2. Power Factor ApparentPower
S
The power Factor in an AC circuit can be calculated by any one of the following
methods
❖ Cosine of angle between V and I
❖ Resistance/Impedance R/Z
❖ Real Power/Apparent Power P/S
Phasor algebra in a RL series circuit
V = V + j0 =V0o
Z = R + jX L
= Z
I =
V
=
V Z Z
P 2 + Q 2

 −
S = VI *
= P + jQ
R-C Series circuit

= 
Consider an AC circuit with a resistance R and a capacitance C connected in series as
shown in the figure. The alternating voltage v is given by
v V sin t
m
The current flowing in the circuit is i. The voltage across the resistor is VR and that
across the capacitor is VC.
VC=IXC lags behind the current by 90 degrees
With the above information, the phasor diagram can be drawn as shown.
The current I is taken as the reference phasor. The voltage VR is in phase with I and
the voltage VC lags behind the current by 90⁰. The resultant voltage V can be drawn as shown in the
figure. Fromthe phasordiagram weobservethat the voltagelagsbehind the currentby an angle Φ or in otherwords
thecurrentleadsthevoltageby anangle Φ.
The waveform and equations for an RC series circuit can be drawn as below.
V = Vm sint
I = Im sin(t + )

C
can be derived as follows.
V =
VR = IR
VC = IXC
V =
V = I
V = IZ
R2
+ X2
Where impedance Z =
Average power
P =VIcos
Hence the power in an RC series circuit is consumed only in the resistance. The
capacitance does not consume any power.
Impedance Triangle
We can derive a triangle called the impedance triangle from the phasor diagram of an
RC series circuit as shown
V 2
+ V2
R C
(IR)2
+ (IX C )
2
R2
+ X 2
C

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Phasor algebra for RC series circuit
V = V + j0 = V0o
Z = R − jXC
= Z −
I =
V
=
V  +
Z Z

R-L-C Series circuit
Consider an AC circuit with a resistance R, an inductance L and a capacitance C
connected in series as shown in the figure. The alternating voltage v is given by
v = Vm sint
The current flowing in the circuit is i. The voltage across the resistor is VR, the voltage
across the inductor is VL and that across the capacitor is VC.
VL=IXL leads the current by 90 degrees
VC=IXC lags behind the current by 90
degrees
With the above information, the phasor diagram can be drawn as shown. The current I
is taken as the reference phasor. The voltage VR is in phase with I, the voltage VL leads
the current by 90⁰ and the voltage VC lags behind the current by 90⁰. There are two cases
that can occur VL>VC and VL<VC depending on the values of XL and XC. And hence there
are two possible phasor diagrams. The phasor VL-VC or VC-VL is drawn and then the
resultant voltage V is drawn.

VL>VC VL<VC
FromthephasordiagramweobservethatwhenVL>VC ,thevoltageleadsthecurrentbyanangle Φorin otherwords
thecurrentlagsbehindthevoltagebyanangleΦ.WhenVL<VC ,thevoltagelagsbehindthe currentbyanangle Φor
inotherwordsthecurrentleadsthevoltagebyanangleΦ.
can be derived as follows.
V =
V =
(IR)2
+ (IX − IX 2
L C )
Where impedance Z =
From the expression for phase angle, we can derive the following three cases
Case (i): When XL>XC
The phase angle Ф is positive and the circuit is inductive. The circuit behaves like a series
RL circuit.
Case (ii): When XL<XC
The phase angle Ф is negative and the circuit is capacitive. The circuit behaves like a
series RC circuit.
VR2 + (VL −VC )2
R2
+ ( X − X 2
L C )

Case (iii): When XL=XC
The phase angle Ф = 0 and the circuit is purely resistive. The circuit behaves like a pure
resistive circuit.
The voltage and the current can be represented by the following equations. The angle Φ
is positive or negative depending on the circuit elements.
V = Vm sint
I = Im sin(t  )
Average power
P = VI cos
P = (IZ )  I 
R
Z
P = I 2
R
Hence the power in an RLC series circuit is consumed only in the resistance. The
inductance and the capacitance do not consume any power.
Phasor algebra for RLC series circuit
V = V + j0 = V0o
Z = R+ j(X L − XC )= Z
I =
V
=
V
Z Z
 −

UNIT-III
Transformers

Limb
or leg
LV
HV
LV
HV
Gaps
INTRODUCTION
Transformer is a static device which transfers electrical energy from one electrical circuitto
another electrical circuit without change in frequency through magnetic medium. The winding which
receives energy is called primary winding and the winding which delivers energy to the load is called
secondary winding.
Based on the voltage levels transformers are classified into two types
i. Step down transformer ii. Step up transformer.
CONSTRUCTION
CORE-TYPE AND SHELL-TYPE CONSTRUCTION
Depending upon the manner in which the primary and secondary windings are placed on the core, and
the shape of the core, there are two types of transformers, called (a) core type, and (b) shell type. In core
type transformers, the windings are placed in the form of concentric cylindrical coils placed around the
vertical limbs of the core. The low-voltage (LV) as well as the high-voltage (HV) winding are made in
two halves, and placed on the two limbs of core. The LV winding is placed next to the core for economy
in insulation cost. Figure a shows the cross-section of the arrangement. In the shell type transformer, the
primary and secondary windings are wound over the central limb of a three-limb core as shown in Figure
b. The HV and LV windings are split into a number of sections, and the sections are interleaved or
sandwiched i.e. the sections of the HV and LV windings are placed alternately.
H.V. winding
Core
L.V. Winding
(a) core type (b) Shell Type
CORE
The core is built-up of thin steel laminations insulated from each other. This helps in reducing the eddy current
losses in the core, and also helps in construction of the transformer. The steel used for core is of high silicon content,
sometimes heat treated to produce a high permeability and low hysteresis loss. The material commonly used for core

is CRGO (Cold Rolled Grain Oriented) steel.
Conductor material used for windings is mostly copper. However, for small distribution transformer
aluminium is also sometimes used. The conductors, core and whole windings are insulated using various insulating
materials depending upon the voltage.
INSULATING OIL
In oil-immersed transformer, the iron core together with windings is immersed in insulating oil. The insulating oil
provides better insulation, protects insulation from moisture and transfers the heat produced in core and windings
to the atmosphere. The transformer oil should posses the following quantities:
(a) High dielectric strength,
(b) Low viscosity and high purity,
(c) High flash point, and
(d) Free from sludge.
Transformer oil is generally a mineral oil obtained by fractional distillation of crude oil.
TANK AND CONSERVATOR
The transformer tank contains core wound with windings and the insulating oil. In large transformers small
expansion tank is also connected with main tank is known as conservator. Conservator provides space when
insulating oil expands due to heating. The transformer tank is provided with tubes on the outside, to permits
circulation of oil, which aides in cooling. Some additional devices like breather and Buchholz relay are connected
with main tank.
Buchholz relay is placed between main tank and conservator. It protect the transformer under extreme heating
of transformer winding. Breather protects the insulating oil from moisture when the cool transformer sucks air
inside. The silica gel filled breather absorbs moisture when air enters the tank. Some other necessary parts are
connected with main tank like, Bushings, Cable Boxes, Temperature gauge, Oil gauge, Tapings, etc.
WORKING PRINCIPLE
In its simplest form a single-phase transformer consists of two windings, wound on an iron
core one of the windings is connected to an ac source of supply f. The source supplies a current to this winding
(called primary winding) which in turn produces a flux in the iron core. This flux is alternating in nature If the
supplied voltage has a frequency f, the flux in the core also alternates at a frequency f. the alternating flux linking
with the second winding, induces a voltage E2 in the second winding (according to faraday‟s law). [Note that this
alternating flux linking with primary winding will also induce a voltage in the primary winding, denoted as E1.
Applied voltage V1 is very nearly equal to E1]. If the number of turns in the primary and secondary windings is N1
and N2 respectively, we shall see later in this unit that E1/N1 = E2/N2. The load is connected across the secondary
winding, between the terminals a1, a2. Thus, the load can be supplied at a voltage higher or lower than the supply

voltage, depending upon the ratio N1/N2.
IDEAL TRANSFORMER
Under certain conditions, the transformer can be treated as an ideal transformer. The assumptions
necessary to treat it as an ideal transformer are :
(a) Primary and secondary windings have zero resistance. This means that ohmic loss (I2
R
loss), and resistive voltage drops in windings are zero.
(b) There is no leakage flux, i.e. the entire flux is mutual flux that links both the primary and
secondary windings.
(c) Permeability of the core is infinite this means that the magnetizing current needed for
establishing the flux is zero.
(d) Core loss (hysteresis as well as eddy current losses) are zero.
IDEAL TRANSFORMER ON NO LOAD

IDEAL TRANSFORMER ON LOAD
V1/V2=N1/N2=I1/I2
EQUIVALENT CIRCUIT OF REAL TRANSFORMER
REGULATION OF TRANSFORMER
Voltage regulation of a transformer is defined as the drop in the magnitude of load voltage (or secondary
terminal voltage) when load current changes from zero to full load value. This is expressed as a fraction of
secondary rated voltage
(%) Regulation = (Secondary terminal voltage at no load − Secondary terminal voltage at any load)/ secondary
rated voltage.
Percentage voltage regulation =(V-E0)*100/V
LOSSES AND EFFICIENCY OF TRANSFORMER
A transformer does‟t contains any rotating part so it is free from friction and windage losses.

1 R
η i c
2
In transformer the losses occur in iron parts as well as in copper coils. In iron core the losses are sum of hysteresis
and eddy current losses. The hysteresis losses are
Ph α f Bx
max and eddy current loss is equal to Pe α f2
Bmax.
Where “f” is frequency “Bmax” is maximum flux density.
IRON LOSSES OR CORE LOSSES
To minimize hysteresis loss in transformer, we use Cold Rolled Grain Oriented (CRGO) silicon steel to
build up the iron core.
EDDY CURRENT LOSS
When the primary winding variable flux links with iron core then it induces some EMF on the surface of core. The
magnitude of EMF is different at various points in core. So, there is current between different points in Iron Core
having unequal potential.
These currents are known at eddy currents. I2
R loss in iron core is known as eddy current loss. These losses depend
on thickness of core. To minimize the eddy current losses we use the Iron Core which is made of laminated sheet
stampings. The thickness of stamping is around 0.5 mm.
COPPER LOSSES
In a transformer the primary and secondary winding currents increase with increases in load. Due to these
currents there is some I2
R losses. These are known as copper losses or ohmic losses. The total I2
R loss in both
windings at rated or full load current is equal to I 2
R1 = I 2
2 .
EFFICIENCY OF SINGLE PHASE TRANSFORMER
Efficiency (η)= output power/input power
=(input power –total losses)/input power
Alternatively η= output power/(output power + total losses)
In a transformer, if Pi is the iron loss, and Pc is the copper loss at full load (when the load current is equal to the
rated current of the transformer, the total losses in the transformer are Pi + Pc. In any transformer, copper losses are
variable and iron losses are fixed.
When the load on transformer is x times full load then
η = x V2 I2 cos φ/( x V2 I2 cos φ+Pi+x2*
Pc)
or
= x KVA cos φ/( x KVA cos φ+P +x2*
P )
OPEN CIRCUIT TEST
Practically we can determine the iron losses by performing the open circuit test and also the core loss
components of equivalent circuit.
We perform open circuit test in low voltage winding in transformer keeping the high voltage winding open. The
circuit is connected as shown in Figure. The instruments are connected on the LV side. The advantage of performing
the test from LV side is that the test can be performed at rated voltage.
When we apply rated voltage then watt meter shows iron losses [There is some copper loss but this
is negligible when compared to iron loss]. The ammeter shows no load current I0 which is very small
[2-5 % of rated current]. Thus, the drops in R1 and Xl1 can be neglected.

We have W0= iron loss
I0= no load current
Then cos φ =
W
0
V
iI
0
So I e = I 0 cos φ
And I m = I 0 sin φ .
R0= Vi/Ie
X0= Vi/Im
SHORT CIRCUIT TEST
From short circuit test we can determine copper losses and also the winding components of equivalent circuit.
It‟s an indirect method to find out the copper losses. To perform this test, we apply a reduced voltage to the primary
winding through instruments keeping LV winding short circuited. The connections are shown in Figure. We need to
apply only 5-10% of rated voltage to primary to circulated rated current in the primary and secondary winding. The
applied voltage is adjusted so that the ammeter shows rated current of the winding. Under this condition, the watt-
meter reading shows the copper losses of the transformer. Because of low value of applied voltage, iron losses, are
very small and can be neglected.

Connection diagram for short circuit test
Equivalent circuit under shot circuit
At a rated current watt meter shows full load copper loss. We have
Wsc= copper loss
Isc = full load current
Vsc =supply voltage
Req =Wsc/Isc
2
Z
eq= Vsc/Isc
Xeq = ⱱ(Zeq
2
- Req
2
)
and equivalent impedance
So we calculate equivalent reactance. These Req and Xeq are equivalent resistance and reactance of both
windings referred in HV side. These are known as equivalent circuit resistance and reactance.

UNIT-IV
DC GENERATOR
Introduction:
The electrical machines deals with the energy transfer either from mechanical to electrical form
or from electrical to mechanical form, this process is called electromechanical energy conversion.
An electrical machine which converts mechanical energy into electrical energy is called an
electric generator while an electrical machine which converts electrical energy into the
mechanical energy is called an electric motor. A DC generator is built utilizing the basic principle
that emf is induced in a conductor when it cuts magnetic lines of force. A DC motor works on the
basic principle that a current carrying conductor placed in a magnetic field experiences a force.
Working principle:
All the generators work on the principle of dynamically induced emf. The change in flux
associated with the conductor can exist only when there exists a relative motion between the

conductor and the flux. The relative motion can be achieved by rotating the conductor w.r.t flux
or by rotating flux w.r.t conductor. So, a voltage gets generated in a conductor as long as there
exists a relative motion between conductor and the flux. Such an induced emf which is due to
physical movement of coil or conductor w.r.t flux or movement of flux w.r.t coil or conductor is
called dynamically induced emf. Whenever a conductor cuts magnetic flux, dynamically induced
emf is produced in it according to Faraday‟s laws of Electromagnetic Induction. This emf causes
a current to flow if the conductor circuit is closed.In a practical generator, the conductors are
rotated to cut the magnetic flux, keeping flux stationary. To have a large voltage as output, a
number of conductors are connected together in a specific manner to form a winding. The
winding is called armature winding of a dc machine and the part on which this winding is kept is
called armature of the dc machine. The magnetic field is produced by a current carrying winding
which is called field winding.The conductors placed on the armature are rotated with the help of
some external device. Such an external device is called a prime mover. The commonly used
prime movers are diesel engines, steam engines, steam turbines, water turbines etc. The purpose
of the prime mover is to rotate the electrical conductor as required by Faraday‟s laws The
direction of induced emf can be obtained by using Flemings right hand rule. The magnitude of
induced emf = e = BLV sin = Emsin . The nature of the induced emf for a conductor rotating
in the magnetic field is alternating. As conductor rotates in a magnetic field, the voltage
component at various positions is different. Hence the basic nature of induced emf in the armature
winding in case of dc generator is alternating. To get dc output which is unidirectional, it is
necessary to rectify the alternating induced emf. A device which is used in dc generator to
convert alternating induced emf to unidirectional dc emf is called commutator.
Construction of DC machines: A D. C. machine consists of two main parts
1. Stationary part: It is designed mainly for producing a magnetic flux.
2. Rotating part: It is called the armature, where mechanical energy is converted into
electrical (electrical generate) or conversely electrical energy into mechanical (electric
into)
Parts of a Dc Generator:
The stationary parts and rotating parts are separated from each other by an air gap. The
stationary part of a D. C. machine consists of main poles, designed to create the magnetic flux,
commutating poles interposed between the main poles and designed to ensure spark less
operation of the brushes at the commutator and a frame / yoke. The armature is a cylindrical body
rotating in the space between the poles and comprising a slotted armature core, a winding inserted
in the armature core slots, a commutator and brush
Yoke:

It saves the purpose of outermost cover of the dc machine so that the insulating materials
get protected from harmful atmospheric elements like moisture, dust and various gases like SO2,
acidic fumes etc. It provides mechanical support to the poles. It forms a part of the magnetic
circuit. It provides a path of low reluctance for magnetic flux. Choice of material: To provide low
reluctance path, it must be made up of some magnetic material. It is prepared by using cast iron
because it is the cheapest. For large machines rolled steel or cast steel, is used which provides
high permeability i.e., low reluctance and gives good mechanical strength.
Poles: Each pole is divided into two parts
a) pole core b) pole shoe
Pole core basically carries a field winding which is necessary to produce the flux. It directs the flux
produced through air gap to armature core to the next pole. Pole shoe enlarges the area of armature core to
come across the flux, which is necessary to produce larger induced emf. To achieve this, pole core has
been given a particular shape. Choice of material: It is made up of magnetic material like cast iron or cast
steel. As it requires a definite shape and size, laminated construction is used. The laminations of required
size and shape are stamped together to get a pole which is then bolted to yoke.
Armature: It is further divided into two parts namely,
(1) Armature core (2) Armature winding.
Armature core is cylindrical in shape mounted on the shaft. It consists of slots on its periphery
and the air ducts to permit the air flow through armature which serves cooling purpose.

Armature core provides house for armature winding i.e., armature conductors. To provide a path of low
reluctance path to the flux it is made up of magnetic material like cast iron or cast steel. Choice of
material: As it has to provide a low reluctance path to the flux, it is made up of magnetic material like cast
iron or cast steel.It is made up of laminated construction to keep eddy current loss as low as possible.A
single circular lamination used for the construction of the armature core is shown below.
Armature winding:
Armature winding is nothing but the inter connection of the armature conductors, placed in the
slots provided on the armature core. When the armature is rotated, in case of generator magnetic
flux gets cut by armature conductors and emf gets induced in them.Generation of emf takes place
in the armature winding in case of generators.To carry the current supplied in case of dc motors.
To do the useful work it the external circuit.
Choice of material: As armature winding carries entire current which depends on external load.it
has to be made up of conducting material, which is copper
Field winding:
The field winding is wound on the pole core with a definite direction.
Functions: To carry current due to which pole core on which the winding is placed behaves as an
electromagnet, producing necessary flux. As it helps in producing the magnetic field i.e. exciting
the pole as electromagnet it is called ‘Field winding’ or „Exciting winding’.
Choice of material: As it has to carry current it should be made up of some conducting material
like the aluminum or copper. But field coils should take any type of shape should bend easily, so
copper is the proper choice. Field winding is divided into various coils called as field coils. These
are connected in series with each other and wound in such a direction around pole cores such that
alternate N and S poles are formed.
Commutator: The rectification in case of dc generator is done by device called as commutator.
Functions: To facilitate the collection of current from the armature conductors. To convert internally
developed alternating emf to in directional (dc) emf .To produce unidirectional torque in case of motor.
Choice of material: As it collects current from armature, it is also made up of copper segments. It is
cylindrical in shape and is made up of wedge shaped segments which are insulated from each other by
thin layer of mica.
Brushes and brush gear: Brushes are stationary and rest on the surface of the Commutator.
Brushes are rectangular in shape. They are housed in brush holders, which are usually of box
type. The brushes are made to press on the commutator surface by means of a spring, whose
tension can be adjusted with the help of lever. A flexible copper conductor called pigtail is used
to connect the brush to the external circuit.
Functions: To collect current from commutator and make it available to the stationary external
circuit.Choice of material: Brushes are normally made up of soft material like carbon.
Bearings: Ball-bearings are usually used as they are more reliable. For heavy duty machines,
roller bearings are preferred.

Types of armature winding
Armature conductors are connected in a specific manner called as armature winding and
according to the way of connecting the conductors; armature winding is divided into two types.
Lap winding: In this case, if connection is started from conductor in slot 1 then the connections
overlap each other as winding proceeds, till starting point is reached again.
There is overlapping of coils while proceeding. Due to such connection, the total number of
conductors get divided into „P‟ number of parallel paths, where
P = number of poles in the machine.
Large number of parallel paths indicate high current capacity of machine hence lap winding is
pertained for high current rating generators.
Wave winding: In this type, winding always travels ahead avoiding over lapping. It travels like a
progressive wave hence called wave winding. Both coils starting from slot 1 and slot 2
areprogressing in wave fashion.Due to this type of connection, the total number of conductors get
divided into two number of parallel paths always, irrespective of number of poles of machine.
EMF equation
EMF generated/path = PN/60 (Z/P) = ZN/60
Z = total number of armature conductors.
= number of slots x number of conductors/slot
N = armature rotation in revolutions (speed for armature) per minute (rpm) A =No.
of parallel paths into which the „z‟ no. of conductors are divided.
E = emf induced in any parallel path
Eg = emf generated in any parallel path
A = 2 for simplex – wave winding
A =P for simplex lap-winding
DC MOTOR
A dc motor is similar in construction to a dc generator. As a matter of fact a dc generator will run as a
motor when its field & armature windings are connected to a source of direct current.
The basic construction is same whether it is generator or a motor.
Working principle:
The principle of operation of a dc motor can be stated as when a current carrying conductor is
placed in a magnetic field; it experiences a mechanical force. In a practical dc motor, the field winding
produces the required magnetic held while armature conductor play the role of current carrying conductor
and hence the armature conductors experience a force.As conductors are placed in the slots which are on
the periphery, the individual force experienced by the conductive acts as a twisting or turning force on the
armature which is called a torque.The torque is the product of force and the radius at which this force
acts, so overall armature experiences a torque and starts rotating.Consider a single conductor placed in a

magnetic field , the magnetic field is produced by a permanent magnet but in practical dc motor it is
produced by the field winding when it carries a current.Now this conductor is excited by a separate supply
so that it carries a current in a particular direction. Consider that it carries a current away from an current.
Any current carrying conductor produces its own magnetic field around it, hence this conductor also
produces its own flux, around. The direction of this flux can be determined by right hand thumb rule. For
direction of current considered the direction of flux around a conductor is clock-wise. Now, there are two
fluxes present
1. Flux produced by permanent magnet called main flux
2. Flux produced by the current carrying conductor
From the figure shown below, it is clear that on one side of the conductor, both the fluxes are in the same
direction in this case, on the left of the conductor there gathering of the flux lines as two fluxes help each
other. A to against this, on the right of the conductor, the two fluxes are in opposite direction and hence
try to cancel each other. Due to this, the density of the flux lines in this area gets weakened.
So on the left, there exists high flux density area while on the right of the conductor then exists low flux
density area The flux distribution around the conductor arts like a stretched ribbed bond under tension.
The exerts a mechanical force on the conductor which acts from high flux density area towards low flux
density area, i.e. from left to right from the case considered as shown above.
In the practical dc motor, the permanent magnet is replaced by the field winding which produces the
required flux winding which produces the required flux called main flux and all the armature conductors,
would on the periphery of the armature gram, get subjected total he mechanical force.
Due to this, overall armature experiences a twisting force called torque and armature of the motor status
rotating.
Direction of rotation of motor
The magnitude of the force experienced by the conductor in a motor is given by F = BIL newtons.The
direction of the main field can be revoked y changing the direction of current passing through the field
winding, which is possible by interchanging the polarities of supply which is given to the field
winding.The direction of current through armature can be reversed by changing supply polarities of dc
supplying current to the armature.
It directions of both the currents are changed then the direction of rotation of the motor remains
undamaged. In a dc motor both the field and armature is connected to a source of direct current. The
current through the armature winding establish its own magnetic flux the interaction both the main field
and the armature current produces the torque, there by sensing the motor to rotate, once the motor starts
rotating, already existing magnetic flux there wire be an induced emf in the armature conductors due to
generator action. This emf acts in a direction apposite to supplied voltage. Therefore it is called Black
emf.
Significance of Back emf

In the generating action, when a conductor cuts the lines of flux, emf gets induced in the conductor in a
motor, after a motoring action, armature starts rotating and armature conductors cut the main flux. After a
motoring action, there exists a generating action there is induced emf in the rotating armature conductors
according to Faraday‟s law of electromagnetic induction. This induced emf in the armature always acts in
the opposite direction of the supply voltage. This is according tot he lenz‟s law which states that the
direction of the induced emf is always so as to oppose the case producing it. In a dc motor, electrical input
i.e., the supply voltage is the cause and hence this induced emf opposes the supply voltage.The emf tries
to set u a current throughout he armature which is in the opposite direction to that which supply voltage is
forcing through the conductor so, as this emf always opposes the supply voltage, it is called back emf and
devoted as Eb. Through it is denoted as Eb, basically it gets generated by the generating action which we
have seen
=  ZNP
60 A
Voltage equation of a Motor
The voltage v applied across the motor armature has to (1) over core the back emf Eb and
3. supply the armature ohmic drop Ia Ra
v = Eb + Ia Ra
This is known as voltage equation of a motor
Torque: The turning or twisting movement of a body is called Torque
Tsh =output/((2∏N)/60)
Tsh =9.55(output)/N

INTRODUCTION TO POLY PHASE INDUCTION MOTORS
Three-phase induction motors are the most common and frequently encountered machines in industry.
– simple design, rugged, low-price, easy maintenance
– wide range of power ratings: fractional horsepower to 10 MW
– run essentially as constant speed from no-load to full load
– Its speed depends on the frequency of the power source
• not easy to have variable speed control
• requires a variable-frequency power-electronic drive for optimal speed control.
CONSTRUCTION DETAILS OF INDUCTION MOTOR
An induction motor has two main parts
– a stationary stator
• consisting of a steel frame that supports a hollow, cylindrical core
• core, constructed from stacked laminations (why?), having a number of evenly
spaced slots, providing the space for the stator winding .

Fig: STATOR OF INDUCTION MOTOR
a revolving rotor
• composed of punched laminations, stacked to create a series of rotor slots,
providing space for the rotor winding
• one of two types of rotor windings
• conventional 3-phase windings made of insulated wire (wound-rotor) » similar to
the winding on the stator
•
Aluminum bus bars shorted together at the ends by two aluminum rings, forming
a squirrel-cage shaped circuit (squirrel-cage).
CONSTRUCTION OF CAGE AND WOUND ROTOR MACHINES
Two basic design types depending on the rotor design
Squirrel-cage: conducting bars laid into slots and shorted at both ends by shorting rings.
Wound-rotor: complete set of three-phase windings exactly as the stator. Usually Y-connected, the ends
of the three rotor wires are connected to 3 slip rings on the rotor shaft. In this way, the rotor circuit is
accessible.

Fig:- Squirrel cage rotor
Fig: Wound rotor

Fig:- Cutaway in a typical wound-rotor IM.
PRODUCTION OF ROTATING MAGNETIC FIELD
• Balanced three phase windings, i.e. mechanically displaced 120 degrees from each other, fed by
balanced three phase source
• A rotating magnetic field with constant magnitude is produced, rotating with a speed
NS=120f/p
Where fe is the supply frequency and
iR = I m cos ωt
iY = I m cos (ωt −120°)
iB = I m cos (ωt +120°) = I m cos (ωt − 240°)
Please note that the phase sequence is R-Y-B. I m is the maximum value of the phase currents, and,
as the phase currents are balanced, the rms values are equal ( I R = IY = I B )
Three pulsating mmf waves are now set up in the air- gap, which have a time phase difference of 120°
from each other. These mmfs are oriented in space along the magnetic axes of the phases, R, Y & B, as
illustrated by the concentrated coils in Fig. 29.2. Please note that 2-pole stator is shown, with the angle
between the adjacent phases, R & Y as 120°, in both mechanical and electrical terms. Since the magnetic
axes are located 120° apart in space from each other, the three mmf‟s are expresses mathematically as
FR = Fm cos ωt cos θ
FY = Fm cos (ωt −120°) cos (θ −120°) FB = Fm cos
(ωt +120°) cos (θ +120°)

Wherein it has been considered that the three mmf waves differ progressively in time phase by 120°, i.e.
2π / 3 rad (elect.), and are separated in space phase by 120°, i.e.
2π / 3 rad (elect.). The resultant mmf wave, which is the sum of three pulsating mmf waves, is
F = FR + FY + FB
Substituting the values,
(θ, t)
4. Fm [cos ωt cos θ + cos (ωt −120°) cos (θ −120°) + cos (ωt +120°) cos (θ +120°)] The first term of
this expression is
cos ω t cos θ = 0.5 [cos (θ −ω t) + cos (θ +ω t)]
The second term is
cos (ω t −120°) cos (θ −120°) = 0.5 [cos (θ −ω t) + cos (θ +ω t − 240°)]
Similarly, the third term can be rewritten in the form shown. The
expression is
F (θ, t) = 1.5 Fm cos (θ −ω t)
+ 0.5 Fm [cos (θ +ωt) + cos (θ +ωt − 240°) + cos (θ +ωt + 240°)] Note that
cos (θ +ω t − 240°) = cos (θ +ω t +120°) , and cos (θ +ω
t + 240°) = cos (θ +ω t −120°) .
If these two terms are added, then
cos (θ +ω t +120°) + cos (θ +ω t −120°) = −cos (θ +ω t)
So, in the earlier expression, the second part of RHS within the capital bracket is zero. In other words, this
part represents three unit phasors with a progressive phase difference of 120°, and therefore add up to
zero. Hence, the resultant mmf is
F (θ,t) =1.5 Fm cos (θ −ωt)
The peak value of the resultant mmf is Fpeak =1.5 Fm.

P is the no. of poles and nsync is called the synchronous speed in rpm (revolutions per minute).
PRINCIPLE OF OPERATION
• This rotating magnetic field cuts the rotor windings and produces an induced voltage in therotor
windings.
• Due to the fact that the rotor windings are short circuited, for both squirrel cage and wound-rotor,
and induced current flows in the rotor windings
• The rotor current produces another magnetic field
• A torque is produced as a result of the interaction of those two magnetic fields

Where ind is the induced torque and BR and BS are the magnetic flux densities of the rotor and
the stator respectively.
SLIP
S= NS-NR/NS
Where s is the slip
Notice that: if the rotor runs at synchronous speed
s = 0
If the rotor is stationary
s = 1
Slip may be expressed as a percentage by multiplying the above eq. by 100, notice that the slip isa
ratio and doesn‟t have units
ROTOR FREQUENCY
Frequency of the rotor‟s induced voltage at any speed nm is FR
=SFS
• When the rotor is blocked (s=1) , the frequency of the induced voltage is equal to the supply
frequency.
• On the other hand, if the rotor runs at synchronous speed (s = 0), the frequency will be zero.
TORQUE EQUATION
• While the input to the induction motor is electrical power, its output is mechanical power andfor
that we should know some terms and quantities related to mechanical power
• Any mechanical load applied to the motor shaft will introduce a Torque on the motor shaft. This
torque is related to the motor output power and the rotor speed.

TORQUE-SLIP CHARACTERISTICS
1. The induced torque is zero at synchronous speed. Discussed earlier.
2. The curve is nearly linear between no-load and full load. In this range, the rotor resistanceis
much greater than the reactance, so the rotor current, torque increase linearly with theslip.
3. There is a maximum possible torque that can‟t be exceeded. This torque is called pullout torque
and is 2 to 3 times the rated full-load torque.
4. The starting torque of the motor is slightly higher than its full-load torque, so the motor will start
carrying any load it can supply at full load.
5. The torque of the motor for a given slip varies as the square of the appliedvoltage.
If the rotor is driven faster than synchronous speed it will run as a generator, converting mechanical
power to electric power.

UNIT V
Basic Instruments

Principle of instruments:
All electrical measuring instruments depend for their action on one of the many physical effects of
an electric current or potential and are generally classified according to which of these effects is
utilized in their operation. The effects generally utilized are:
1. Magnetic effect-for ammeters and voltmeters usually.
2. Electro dynamic effect-for ammeters and voltmeters usually.
3. Electromagnetic effect-for ammeters, voltmeters ,wattmeters and watt hour meters.
4. Thermal effect-for ammeters and voltmeters.
5. Chemical effect-for d.c.ampere-hour meters.
6. Electro static effect-for voltmeter sonly
Permanent Magnet Moving Coil (PMMC): A moving coil instrument consists basically of a permanent
magnet to provide a magnetic field and a small lightweight coil is wound on a rectangular soft iron core
that is free to rotate around its vertical axis. When a current is passed through the coil windings, a torque
is developed on the coil by the interaction of the magnetic field and the field set up by the current in the
coil. The aluminum pointer attached to rotating coil and the pointer moves around the calibrated scale
indicates the deflection of the coil

Principle of operation: the interaction between the induced field and the field produced by the
permanent magnet causes a deflecting torque, which results in rotation of the coil.
Deflecting Torque:
If the coil is carrying a current of , the force on a coil side = .i amp BilN (newton, N).
∴Torque due to both coil sides =2rBil Nm = Gi Nm
Controlling Torque: The value of control torque depends on the mechanical design of the control device.
For spiral springs and strip suspensions, the controlling torque is directly proportional to the angle of
deflection of the coil.,ie Control torque =Cθ
Damping Torque:
It is provided by the induced currents in a metal former or core on which the coil is wound or in the
circuit of the coil itself. As the coil moves in the field of the permanent magnet, eddy currents are set up
in the metal former or core. The magnetic field produced by the eddy currents opposes the motion of the
coil. The pointer will therefore swing more slowly to its proper position and come to rest quickly with
very little oscillation. Electromagnetic damping is caused by the induced effects in the moving coil as it
rotates in magnetic field, provided the coil forms part of closed electric circuit.
Moving Iron Instruments:
The deflecting torque in any moving-iron instrument is due to forces on a small piece of magnetically
„soft‟ iron that is magnetized by a coil carrying the operating current. In repulsion type moving–iron
instrument consists of two cylindrical soft iron vanes mounted within a fixed current-carrying coil. One
iron vane is held fixed to the coil frame and other is free to rotate, carrying with it the pointer shaft. Two
irons lie in the magnetic field produced by the coil that consists of only few turns if the instrument is an
ammeter or of many turns if the instrument is a voltmeter. Current in the coil induces both vanes to
become magnetized and repulsion between the similarly magnetized vanes produces a proportional
rotation. The deflecting torque is proportional to the square of the current in the coil, making the
instrument reading is a true „RMS‟ quantity Rotation is opposed by a hairspring that produces the
restoring torque. Only the fixed coil carries load current, and it is constructed so as to withstand high
transient current. Moving iron instruments having scales that are nonlinear and some what crowded in the
lower range of calibration.

Attraction type instrument consists of a few soft iron discs (B) that are fixed to the spindle (D), pivoted in
jeweled bearings. The spindle (D) also carries a pointer (P), a balance weight (W1), a controlling weight
(W2) and a damping piston which moves in a curved fixed cylinder (F). The special shape of the moving-
iron discs is for obtaining a scale of suitable form.

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