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Contents
WALKTHROUGH
OBJECTIVES
O B J E C T I V E S
A er completing this Chapter, you will be able to :
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State the meaning of electro-mechanical energy-conversion (EMEC) machines.
Explain how the power flows from a prime-mover to an electrical load by means of a generator.
Explain how the power flows from electric supply to a mechanical load by means of a motor.
State how a generator differs from a motor.
Explain the two ways (alignment and interaction) in which a mechanical force is generated in an
electromechanical system.
State the general characteristics of a synchronous machine.
Derive the expression for synchronous speed in terms of number of poles and frequency of induced
emf.
Describe the construction of stator and rotor of a synchronous machine.
Explain how a rotating magnetic flux is produced by three-phase currents in three windings on
the stator in a synchronous machine.
Explain why a synchronous machine has armature on its stator and field on its rotor.
Derive the expressions for pitch factor and distribution factor.
Derive the expression for induced emf in a generator.
Explain the meaning of ‘armature reaction’ and its effect on generated induced emf.
Draw the equivalent circuit for the stator of an alternator.
Explain the meaning of synchronous reactance (Xs) and synchronous impedance (Zs).
Derive expressions of real power and reactive power generated by a generator.
Describe how to determine the synchronous impedance of a synchronous machine by conducting
open-circuit and short-circuit tests on it.
Determine voltage regulation for lagging and leading power factors.
Explain in what way the operation of a synchronous motor differs from that of a generator, with
the help of suitable phasor diagrams.
Justify that a synchronous motor is a constant-speed motor in true sense.
State different methods of starting a synchronous motor.
Chapter objectives provide a concise statement
of expected learning outcomes.
ADDITIONAL SOLVED EXAMPLES
E X A M PL E
5 . 9
A horizontal overhead line carries a current of 90 A in east-to-west direction. What is the magnitude and direction of
the magnetic field due to this current at a point 1.5 m below the line ?
Solution The magnitude of the magnetic field is given by Eq. 5.2, as
μ I
4 π × 10 − 7 × 90
–6
B= 0 =
= 12 ¥ 10 T = 12 mT
2π x
2 π × 1.5
By applying the right-hand thumb rule, we find that the direction of the magnetic field is from north-to-south.
E X A M PL E
5 . 1 0
What is the magnitude of the magnetic force per unit length on a wire carrying a current of 8 A and making an angle
of 30° with the direction of uniform magnetic field of 0.15 T ?
Solution Using Eq. 5.8, the force per unit length of the wire is given as
Fu =
E X A M PL E
F
= I B sin q = 8 ¥ 0.15 ¥ sin 30° = 0.6 N m –1
l
5 . 1 1
A square coil of side 10 cm consists of 20 turns and carries a current of 12 A. The coil is suspended vertically and
the normal to the plane of the coil makes an angle of 30° with the direction of uniform horizontal magnetic field of
magnitude 0.8 T. What is the magnitude of the torque experienced by the coil ?
S O LV E D E X A M P L E S
Provided at appropriate locations, solved
examples aid in learning the technique of
applying concepts to practical problems.
Solution As shown in Fig. 5.17, the coil MNOP is kept such that the normal to its plane makes an angle of 30° with the
uniform magnetic field. The magnetic force F experienced by each of the sides MN and OP is given by Eq. 5.7, as
F = IBln = 12 ¥ 0.8 ¥ 0.1 ¥ 20 = 19.2 N
The normal distance between these two forces is
x = lsin 30° = 0.1 ¥ 0.5 = 0.05 m
Therefore, the torque experienced by the coil is
t = F x = 19.2 ¥ 0.05 = 0.96 Nm
IR
VRY
I1
I1
30°
–I3
11°34¢
IB
138°26¢
90°
I2
71°34¢
30°
VYB
VBR
I3
I2
11°34
IY
(a)
I2
(b)
(c)
I3
FIGURES
Figures are used exhaustively to illustrate the
concepts and methods described in the text.
Contents
MULTIPLE CHOICE QUESTIONS
Here are some incomplete statements. Four alternatives
are provided below each. Tick the alternative that
completes the statement correctly :
M U LT I P L E C H O I C E
QUESTIONS
Chapter-end MCQs help the students in
clarifying concepts. Also, a useful tool to prepare
for various competitive examinations.
1. The specific resistance r depends upon
(a) the material, the area of cross-section and the
length of the conductor
(b) the area of cross-section and the length of the
conductor only
(c) the area of cross-section of the conductor
only
(d) the nature of the material of the conductor
only
2. The resistance of a conductor increases when
(a) its length increases
(b) its area increases
(c) both its length and area increase
(d) its resistivity is kept constant
3. On increasing its temperature, the resistance of a
conductor made of a metal
(a) decreases
(b) increases
(c) remains constant
(d) varies either
way
xix
5. The ‘ampere second’ could be the unit of
(a) conductance
(b) power
(c) energy
(d) charge
6. The polarity of voltage drop across a resistor is
determined by
(a) the value of the resistor
(b) the value of current through the resistor
(c) the direction of current through the resistor
(d) the polarity of the source
7. If 110 V is applied across a 220-V, 100-W bulb, the
power consumed by it will be
(a) 100 W
(b) 50 W
(c) 25 W
(d) 12.5 W
8. A resistance of 10 W is connected across a supply
of 200 V. When another resistance of R ohms is
connected in parallel with the above 10-W resistor,
the current drawn from the supply doubles. The
value of R is
(a) 5 W
(b) 10 W
(c) 20 W
(d) 40 W
9. Three resistances each of R ohms are connected
in star. Its equivalent delta will comprise three
REVIEW QUESTIONS
1. What is the magnetic field pattern due to a long
current-carrying straight conductor ?
2. When a current-carrying conductor is placed in a
magnetic field, it experiences a force. How do you
find the magnitude and direction of this force ?
3. State and explain (a) Fleming’s left-hand rule, and
(b) Fleming’s right-hand rule.
4. State how you will determine the nature of force
between two parallel current-carrying conductors.
5. Sketch the magnetic field around two adjacent
parallel current-carrying conductors, when the
currents owing through them are (a) in opposite
directions, and (b) in the same direction.
6. Explain how the unit of current is defined.
7. What is a solenoid ? Write the expression for the
magnetic field at a point (a) inside the solenoid, and
(b) just at one of its ends.
8. As you move away from the middle of a solenoid,
why does the magnetic field decrease ?
9. What is the difference between a solenoid and a
toroid ?
10. Suppose that you are sitting in a room with your
back to the wall. Imagine that an electron beam
travelling horizontally from the back wall to the
direction of the magnetic field that exists in the
room ?
11. What is meant by electromagnetic induction ? State
and explain Faraday’s laws of electromagnetic
induction.
12. State Lenz’s law. Show, by means of an example,
that the Lenz’s law and Fleming’s right-hand
rule give the same direction of induced emf in a
circuit.
13. Show that Lenz’s law is a consequence of the
principle of conservation of energy.
14. One end of a bar magnet is thrust into a coil. It
is noted that the induced current in the coil is in
clockwise direction as viewed from the front end.
Is the end of the bar magnet its N-pole or S-pole ?
15. A metallic loop is placed in a nonuniform magnetic
field. Will an emf be induced in the loop ?
16. Two circular loops are placed coaxially but
separated by a distance. A battery is suddenly
connected to one of the loops establishing a current
in it. Will there be a current induced in the other
loop ? Do the loops attract or repel each other ?
17. The battery in the above question is suddenly
disconnected. Is a current induced in the other
REVIEW QUESTIONS
Review questions at the end of each chapter
are meant to give good practice for answering
theoretical questions in examinations.
PROBLEMS
(A)
PROBLEMS WITH
ANSWERS
Problems given at the end of each chapter are
divided, based on the difficulty level, into three
categories—(A) Simple, (B) Tricky, and (C)
Challenging with answers.
SI MP LE
P RO BLEMS
1. If the moving coil of an electric meter consists of
150 turns wound on a square former which has a
length of 4 cm and the ux density in the air gap is
0.06 T, calculate the turning moment acting on the
coil when it is carrying a current of 12 mA.
[Ans. 172.8 ¥ 10 –6 Nm]
2. A moving coil instrument gives a full-scale
deection of 10 mA when the potential difference
across its terminals is 100 mV. Calculate the series
resistance to measure 1000 V on full scale.
[Ans. 99 990 W]
(B)
T RI CKY
3. A moving coil instrument gives a full-scale
deection of 10 mA when a potential difference of
10 mV is applied across its terminals. Show how
will you use the instrument to measure (i) currents
up to 100 A, and (ii) voltage up to 500 V.
[Ans. (i) 0.000 100 01 W; (ii) 49 999 W]
4. A moving coil ammeter has a resistance of 0.01 W
and full scale deection current of 0.25 A. How this
meter can be made to read (i) voltage up to 250 V,
and (ii) current up to 20 A ?
[Ans. (i) 999.99 W; (ii) 1.2658 ¥ 10–4 W]
P RO BLEMS
5. The coil of a moving-iron instrument has a resistance
of 500 W and an inductance of 1 H. An additional
resistance of 2000 W is connected in series with the
instrument to make it a voltmeter. It reads 250
V when a dc voltage of 250 V is applied. What
will it read when 250-V, 50-Hz is applied ?
[Ans. 248 V]
EXPERIMENTAL EXERCISE 10.2
PAR A L L E L
A C
C IR C U IT
Objectives
1. To observe the variation of current I when the resistance in the parallel ac circuit is varied.
2. To draw the phasor diagram for the parallel ac circuit for four sets of impedances obtained by varying the
resistance.
3. To calculate the circuit parameters (R, L and C) for the four sets of observations, assuming the ac supply
frequency to be 50 Hz.
4. To compare the two values of power-factors—one obtained from the readings and the other obtained from the
phasor diagram—for the four sets of observations.
Apparatus Single-phase ac supply; One Variac 0-250 V, 5 A; One choke coil with negligible resistance; One
wattmeter, Three ammeters (MI type) 0-5 A; Three voltmeters (MI Type) 0-300 V; One rheostat 100 W, 5 A.
Circuit Diagram The circuit diagram is shown in Fig. 10.21.
E X P E R I M E N TA L
EXERCISES
Experimental exercies given at the end of relevant
chapters help students to perform laboratory
experiments in a systematic way.
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Contents
C H E C K
YO U R
U N D E R S TA N D I N G
Before you proceed to the next Chapter, take this Test. Give yourself two marks for each correct answer and minus one
for each wrong answer. If your score is 12 or more, go to the next Chapter; otherwise study this Chapter again.
No.
1.
2.
3.
4.
5.
6.
7.
8.
Statement
True
False
The ratio of bandwidth to the resonance frequency of a resonant
circuit is called its quality factor.
In a series resonant circuit, the lower the resistance in the circuit, the
steeper is its current response.
When a capacitor is connected in parallel to an inductive circuit,
the phase angle increases and the power factor decreases.
In a practical resonant circuit, the value of the resistance affects
the resonant frequency.
The impedance of both the series and parallel resonant circuit increase
with increase in frequency.
In a series resonant circuit, the impedance for the frequencies above
resonant frequency is inductive.
When the frequency is much greater than the resonant frequency of
a series resonant circuit, the angle of impedance Z approaches 0°.
For a series resonant circuit, the resonance curve is a plot of frequency
versus voltage.
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Marks
CHECK YOUR
U N D E R S TA N D I N G
A set of 10 objective questions enable students
gauge their mastery of chapter content.
SUMMARY
T ERMS
AN D
CO N CEP T S
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SUMMARY
The chapter-end summary divided into:
(1) Terms and Concepts and (2) Important
Formulae can be used by students for a quick
review during examinations.
Self inductance of a coil arises when an emf is induced in itself by changing the current owing through it.
Isolated inductances in series and parallel are added the same way as resistances.
An inductor may be fixed or variable, iron-cored or air-cored.
When a magnetic field is set up by an inductor, it stores energy.
Mutual inductance is the property of two magnetically coupled coils because of which there is an induced emf in
one coil due to change in current in the other coil.
• Coefcient of coupling (k) is the ratio of ux linkage between primary and secondary coils to the ux produced
by primary current.
• The mutual voltage is present independently of and in addition to any voltage due to self-induction.
• Both L and M are measured in henrys (H).
I MP O RTAN T
FORMULAE
di
.
dt
1 2
LI .
2
• Self-induced emf, e = L
• Energy stored, W =
• EMF induced by mutual inductance, e2 = M
• Coupling coefficient, k =
I M PO R TA NT
di1
.
dt
N2 μ A
.
l
d Φ 21
.
• M21 = N1
di 2
• L=
M
; 0 £ k £ 1.
L1 L2
NO T E
In both the rules—Fleming’s right-hand rule and Fleming’s left-hand rule—the first finger, the central finger and
the thumb represent the same quantities. It may therefore be helpful to associate
First finger
with
Field Flux;
Central finger
with
Current; and
thuMb
with
Motion of the conductor
Often, students get confused which rule to apply where. In electrical engineering, we come across two types of
situations. One may be called generator action, and the other motor action. In generator action, the induced emf
is the result when a conductor is moved in a magnetic field (this is what happens in a dynamo). Whereas, in motor
action, the motion of a conductor is the result when a current is passed through the conductor placed in a magnetic
field (this is what happens in an electric fan).
You can easily remove the confusion by noting that it is your right hand that (usually) generates most of the
things (like writing, painting, tightening of a screw, etc). Thus, for the sake of remembering, the right-hand rule
can be associated with the generator action of the right hand. The other rule (i.e., Fleming’s left-hand rule) then
applies to the motor action.
C O M M O N M I S TA K E S
Wrong concepts or wrong solutions to problems
are deliberately given at many places to
emphasise the mistakes commonly committed by
students.
*MNEMONICS
AID TO MEMORY/
MNEMONICS
By giving examples drawn from day-to-day
experience, aids to memory remove any confusion
from the minds of the students.
As an aid to remember the sequence of colour codes given above,
the student can memorise one of the following (all the capital letters
stand for colours):
(a) Bill Brown Realised Only Yesterday Good Boys Value
Good Work
(b) Bye Bye Rosie Off You Go Bristrol Via Great Western
(c) B B Roy of Great Britain had a Very Good Wife.