Electrical Machines Test - 2 - PDF Flipbook

Electrical Machines Test - 2

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GATE
EEE

Electrical
Machines

Test-02Solutions


ELECTRICAL MACHINES
1. Generally, the no-load losses of an electrical machine is

represented in its equivalent circuit by a
a) parallel resistance with a low value
b) series resistance with a low value
c) parallel resistance with a high value
d) series resistance with a high value
Answer: (a)
Solution:
No-load losses (essentially core losses not F&W losses) are low
and depend upon the applied voltage in an induction machine.
Statement for Linked Answer Question 2:

The figure above shows coils 1 and 2, with dot markings as
shown, having 4000 and 6000 turns respectively. Both the coils
have a rated current of 25 A. Coil 1 is excited with single phase,
400 V, 50 Hz supply.
2. In the autotransformer obtained in statement, the current in each
coil is
a) Coil-1 is 25 A and Coil-2 is 10 A
b) Coil-1 is 10 A and Coil-2 is 25 A
c) Coil-1 is 10 A and Coil-2 is 15 A
d) Coil-1 is 15 A and Coil-2 is 10 A

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Answer: (d)

Solution:

To supply 10 kVA load, I2 = 10×103 = 10
1000

With 10∠θ A in the 6000 turn winding, current in the 4000 turn

winding

1̅ = 6000 × 10∠ = 15∠
4000

3. Neglecting all losses, the developed torque (T) of a d.c

separately excited motor, operating under constant terminal

voltage, is related to its output power (P) as under
a) T ∝ √P

b) T ∝ P
c) T2 ∝ P3

d) T independent of P

Answer: (b)
Solution:
For separately excited motor
ϕ = constant (if armature reaction is neglected and if field
excitation is kept constant)

∝ ⇒ ∝
∝ ⇒ ∝
P is power input. If all losses are neglected, it is also the power
output.

∴ ∝

2


4. Match List-I with List-II with select the correct answer:

List-I List-II

A. Silica Gel 1. Bushing

B. Porcelain 2. Buccholz relay

C. Mercury 3. Tank

D. Fins 4. Breather

Codes:
A BCD

a) 2 1 4 3
b) 4 3 2 1
c) 2 3 4 1
d) 4 1 2 3
Answer: (d)
5. In a transformer, if the iron losses and copper losses are 40.5
kW and 50 kW respectively, then at what fraction of load will
be efficiency be maximum?
a) 0.80
b) 0.57
c) 0.70
d) 0.90

Answer: (d)
Solution:
At minimum efficiency variable loss = fixed loss

2 × ( ) = ⇒ = �4500.5 = 0.9

3


6. A three-winding transformer is connected to an AC voltage

source as shown in the figure. The number of turns are as

follows: N1 = 100, N2 = 50, N3 = 50. If the magnetizing current
is neglected, and the currents in two windings are 2̅ = 2∠300
and 3̅ = 2∠1500 , then what is the value of the current 1̅ , in
amperes?

a) 1∠900

b) 1∠2700

c) 4∠900
d) 4∠2700

Answer: (a)

Solution:

1̅ = 2∠300 50 + 2∠1500 50
100 100

= 1∠300 + 1∠1500

= 1∠900

4


7. A 4-pole, separately excited, wave wound DC machine with

negligible, armature resistance is rated for 230 V and 5 kW at a

speed of 1200 rpm. If the same armature coils are reconnected to

form a lap winding. What is the rated voltage (in volts) and

power (in kW) respectively at 1200 rpm of the reconnected

machine if the field circuit is left unchanged?

a) 230 and 5

b) 115 and 5

c) 115 and 2.5

d) 230 and 2.5

Answer: (b)

Solution:

Total number of conductors = Z

Number of poles P = 4,

Field flux constant = ϕ wb

Rated voltage E = V = 230 V

Wave winding:

Number of parallel paths = A = 2

Speed = 1200 rpm

=
60

= ×1200 4
60 2

× 40 = 230

= 23
4

Rated current = 5000
230

5


Rated current of each conductor = = 250
23

Same winding reconnection as lap winding

Lap winding:

=
60

= ×1200 × 4 = 20( )
60 4

= 20 × 23 = 115
4

Rated current in lap winding = 4 × Rated current of each

conductor

Rated current = 4 × 250 = 1000
23 23

= = 115 × 1000 = 5
23

8. Consider the following statements relating to the constructional

features of a large power transformer:

1. The conservator is used to maintain the level of oil in the

transformer tank.

2. The bushing is used to protect transformer insulation against

lightning over-voltages.

3. The Buchholz relay is an over current relay.

4. Silica gel is used to absorb moisture

Which of these statements are correct?

a) 1, 2, 3 and 4

b) 2 and 3

c) 1 and 4

d) 1, 2 and 4

6


Answer: (c)

Solution:

Bushings are terminals not protective device.

9. A 250 kVA, 11000 V/400 V and 50 Hz single phase transformer

has 80 turns on the secondary, what is the maximum value of

flux?

a) 2475 mWb

b) 0.2 mWb

c) 22.5 mWb

d) 55.2 mWb

Answer: (c)

Solution:

= √2 ℎ

= 400
√2 ×50×80

= 22.5

Statement for Linked Answer Question 10:

A 3-phase, 440 V, 50 Hz, 4 pole, slip ring induction motor is

feed from the rotor side through an auto transformer and the

stator is connected to a variable resistance as shown in the

figure.

7


The motor is coupled to a 220 V, separately excited d.c
generator feeding power to fixed resistance of 10 Ω. Two
wattmeter method is used to measure the input power to
induction motor. The variable resistance is adjusted such that
motor runs at 1410 rpm and the following reading were recorded
W1 = 1800W, W2 = -200W.
10. The Speed of rotation of stator magnetic field with respect to
rotor structure will be
a) 90 rpm in the direction of rotation
b) 90 rpm in the opposite direction of rotation
c) 1500 rpm in the direction of rotation
d) 1500 rpm in the opposite direction of rotation
Answer: (d)
Solution:
With 4 poles and 50Hz, the synchronous speed is 1500 rpm. It is
the rotor which receives the supply, so the rotor mmf rotates at
1500 rpm with respect to the rotor, in a direction determined by
the phase sequence of the rotor supply. Let this direction be

8


clockwise. Then the rotor mmf rotates at 1500 rpm clockwise
with respect to rotor. The stator mmf and rotor mmf rotate in the
same direction and at the same speed, and are hence stationary
with respect to each other. So the stator mmf also rotates in cw
at 1500 rpm with respect to rotor. The rotor itself rotates in
anticlockwise direction at a speed slightly less than the
synchronous speed.
11. What is the efficiency of an auto-transformer in comparison to
that of a two-winding transformer of the same rating?
a) Slightly less than that of a two-winding transformer
b) Same as that of a two-winding transformer
c) More than that of a two-winding transformer
d) As low as 1/5th of the efficiency of a two winding transformer
Answer: (c)
12. The percentage resistance and reactance of a transformer are
2% and 4% respectively. The approximate regulation on full
load at 0.8 pf lag is
a) 12 %
b) 8 %
c) 6 %
d) 4 %
Answer: (d)
Solution:
% V.R = [(%R) × cosϕ ± (%X) × sin ϕ]

= 2 × 0.8 + 4 × 0.6 = 4 (or) V.R = 4%

9


13. Two transformers of identical voltage but of different capacities

are operating in parallel. For satisfactory load sharing

a) impedances must be equal

b) per-unit impedances must be equal

c) per-unit impedances and X/R ratios must be equal

d) impedances and X/R ratios must be equal

Answer: (c)

Solution:

When p.u impedances (on their own ratings as base) are equal,

they share a load in proportion to their VA ratings. If (x/r) ratios

are equal, their full load kVA output is equal to the sum of their

individual VA ratings. (This result can be proved by drawing a

phasor diagram).

14. The rotor power output of 3-phase induction motor is 15 kW.

The rotor copper losses at a slip of 4% will be

a) 600 W

b) 625 W

c) 650 W

d) 700 W

Answer: (b)

Solution:

= 3 22 2 �1− �
15 × 1000 = (3 22 2) ∙ �00..0964�

⇒ 3 22 2 = 625

10


15. A synchronous motor operates at 0.8 p.f. lagging. If the field
current of the motor is continuously increased
1. the power factor decreases upto a certain value of field
current and thereafter it increases
2. the armature current increases upto a certain value of field
current and thereafter it decreases
3. the power factor increases upto a certain value of field current
and thereafter it decreases
4. the armature current decreases upto a certain value of field
current and thereafter it increases. From these the correct one
is
a) 1, 2
b) 2, 3
c) 3, 4
d) 1, 3
Answer: (c)
Solution:

Power factor increases to maximum value later onwards
decreases Ia decreases to minimum value, later onwards
increases.

11


16. An induction motor having 8 poles runs at 727.5 rpm. If the

supply frequency is 50 Hz, the emf in the rotor will have a

frequency of

a) 1.5 Hz

b) 48.5 Hz

c) 51.5 Hz

d) 75 Hz

Answer: (a)

Solution:

= 120×50 = 750
8

∴ = 750−727.5 = 0.03
750

∴ Slip frequency of rotor emf = sf

= 0.03 × 50 = 1.5 Hz

17. If the voltage applied to a transformer primary is increased by

keeping the V/f ratio fixed, then the magnetizing current and the

core loss will respectively,

a) decrease and remain the same

b) increase and decrease

c) remain the same and remain the same

d) remain the same and increase

Answer: (d)

Solution:

Magnetizing flux ∅ ∝ but core loss depends upon the


frequency.

12


18. The injected e.m.f in the rotor of induction motor must have
a) The same frequency as the slip frequency
b) The same phase as the rotor e.m.f
c) A high value for satisfactory speed control
d) The same phase as the rotor e.m.f and a high value for
satisfactory speed control
Answer: (a)
Solution:
Emf injection in the rotor is used to control its speed as well as
power factor.

19. Assertion (A): A double-cage induction motor has good
starting characteristics.
Reason (R): At starting, a large portion of starting current flows
in the bottom cage.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is NOT the correct explanation
of A.
c) A is true but R is false.
d) A is false but R is true.
Answer: (c)
Solution:
At starting, a large portion of starting current flows in the top
cage.

13


20. The flux per pole in a synchronous motor with the field circuit
ON and the stator disconnected from the supply is found to be
25 mWb. When the stator is connected to the rated supply with
the field excitation unchanged, the flux per pole in the machine
is found to be 20 mWb while the motor is running on no load.
Assuming no load losses to be zero, the no load current drawn
by the motor from the supply
a) lags the supply voltage
b) leads the supply voltage
c) is in phase with the supply voltage
d) is zero
Answer: (b)
Solution:
When stator disconnected from the supply Ia = 0, ϕa = 0
Without armature flux, the air gap flux
= ± = 25
With armature flux, the air gap flux
= ± = 20
So the armature flux is causing demagnetizing effect in motor.
Hence the motor is operating with leading power factor.

21. A single-phase two winding transformer is designed to operate
at 400/200 V, 50 Hz. If the h.v side is now energized from a
400V, 40 Hz source, the no-load l.v side voltage would be
a) 300 V
b) 250 V

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c) 200 V
d) 150 V
Answer: (c)
Solution:
As the transformer is designed for 400/200V, the no-load LV
side voltage will be 200 V only.
22. Two transformers when operating in parallel will share the
load depending upon which of the following?
a) Magnetizing current
b) Leakage reactance
c) Per unit impedance
d) Efficiency
Answer: (c)
Solution:
Load sharing not depend on ղ and magnetizing current,
Equivalent impedance also have resistance so option B. Leakage
reactance is also not correct.
23. Consider the following statements:
In a transformer, an iron core is used to
1. Increase the useful flux
2. Reduce the leakage flux
3. Reduce the useful flux
Which of the above is/are correct?
a) 2 only
b) 1 and 2

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c) 2 and 3
d) 3 only
Answer: (b)
Solution:
Iron increases the useful flux and reduces leakage flux.
24. Assertion (A): In a transformer, open circuit (OC) test is
conducted from low voltage side and short circuit (SC) test
conducted froth high voltage side.
Reason (R): OC test gives iron loss and SC test gives copper
loss.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is NOT the correct explanation

of A.
c) A is true but R is false.
d) A is false but R is true.
Answer: (b)
25. When a transformer is first energized, the transient current
during first few cycles, is
a) less than full load current
b) equal to full load current
c) equal to no load current
d) much higher than full load current
Answer: (d)

16


Solution:

When a transformer is first energized it draws large magnetic

inrush current which is having dominant second harmonic upto

20%. This transient current is 5 times the full load current.

26. In a transformer, Pi is iron loss at rated voltage and P. is full

load copper loss. If the maximum efficiency occurs at 75% of

full load, then which one of the following is correct?

a) Pi = Pc

b) 3/4 Pi = Pc

c) 9/16 Pi = Pc

d) 16/9 Pi = Pc

Answer: (d)

Solution:

For maximum efficiency,

Copper loss = Iron loss

Copper loss at 75% full load = (0.75)2

Iron loss at rated voltage = Pi

So, = (0.75)2

= 9
16

= 16
9

27. What is the core loss in a high frequency ferrite core

transformer used in SMPS power supply?

a) 10% of rated power

b) 5% of rated power

17


c) 2% of rated power
d) 1% of rated power
Answer: (d)
Solution:
Core losses will be lesser in case of using high frequency ferrite
core.
28. Assertion (A): Magnetizing current of a single phase
transformer with sinusoidal supply voltage is non-sinusoidal.
Reason (R): Magnetization characteristics of transformer core
is non-linear.
a) Both A and R are true, and R is the correct explanation of A.
b) Both A and R are true, but R is not a correct explanation of

A.
c) A is true, but R is false.
d) A is false, but R is true.
Answer: (a)
Solution:
Due to saturation and hysteresis magnetizing current will be
non-sinusoidal for sinusoidal flux and sinusoidal supply.
29. The full-load copper loss and iron loss of a transformer are
6400 W and 5000 W, respectively. What are the above copper
loss and iron loss, respectively at half-load?
a) 3200 W, 2500 W
b) 3200 W, 5000 W
c) 1600 W, 1250 W

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d) 1600 W, 5000 W
Answer: (d)
Solution:
Iron losses not change due to load variations copper losses ∝
(loading in p u.)2.
30. Which one of the following statements for a dc machine which
is provided with interpole windings (IW) as well as
compensating winding (CW) is correct?
a) Both IW and CW are connected in series with the armature

winding.
b) Both IW and CW are connected in parallel with the armature

winding.
c) IW is connected in series but CW is connected in parallel

with the armature winding.
d) IW is connected in parallel but CW is connected in series

with the armature winding.
Answer: (a)
Solution:
More armature current implies severe armature reaction. To
counter act the effect of armature reaction, IW and CW are
connected in series with armature winding so that for high
armature reaction mmf, action of IW and CW are prominent.

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