Electrical Machines Test - 1 - PDF Flipbook
Electrical Machines Test - 1
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1. What is the maximum efficiency (in %) at unity pf load?
% of F.L at which ηmax occurs = � = 0.696
% = 0.696×300×103×1 × 100
2. The excitation voltage and load angle will respectively be
a) 0.8 pu and 36.86 degrees’ lag
b) 0.8 pu and 36.86 degrees’ lead
c) 1.17 pu and 30.96 degrees’ lead
d) 1.17 pu and 30.96 degrees’ lag
V = 10 p.u, Ia = 0.6 p.u at UPF, XS = 1.0 P.U
Ra = 0
Excitation voltage E = V – jIaXs
= 1.0 – j 0.6 × 1
3. Conventional power frequency equivalent circuit of a two-coiled
transformer is obtained on the assumption of
a) Equal primary and secondary ampere turns
b) Negligible mutual reactance
c) Uniform voltage drop along the windings
d) Presence of leakage current between the windings
Leakage current between winding (capacitive reactance) is
neglected for power frequency transformer. For high frequency
transformer, leakage current between winding is taken into
4. Two transformers, with equal voltage ratio and negligible
excitation current, connected in parallel, share load in the ratio
of their kVA rating only if their p.u. impedances (based on their
own kVA) are
b) in the inverse ratio of their ratings
c) in the direct ratio of their ratings
d) purely reactive
The currents carried by two transformers (also their kVA
loadings) are proportional to their ratings - if their ohmic
impedances (or their pu impedances on a common base) are
inversely proportional to their ratings or their per unit
impedances on their own ratings are equal. The ratio of
equivalent leakage reactance to equivalent resistance should be
the same for all the transformers.
A difference in this ratio results in a divergence of the phase
angle of the two currents, so that one transformer will be
operating with a higher, and the other with a lower power factor
than that of the total output; as a result, the given active load is
not proportionally shared by them.
5. Armature torque of a d.c motor is a function of which of the
2. Field Flux
3. Armature Current
4. Residual Magnetism
Select the correct answer using the codes given below:
a) 2 and 3
b) 1 and 4
c) 3 and 4
d) 1 and 2
In dc motor ∝ . = .
6. If the wave form of the voltage impressed on the primary of a
Y-Δ bank contains 5th harmonics. What are the wave forms of
the resultant voltages of the primary and the secondary?
a) Peaked Peaked
b) Peaked Flat-topped
c) Flat-topped Peaked
d) Flat-topped Flat-topped
7. A separately excited dc machine is coupled to a 50 Hz, three-
phase, 4-pole induction machine as shown in the figure. The dc
machine is energized first and the machines rotate at 1600 rpm.
Subsequently the induction machine is also connected to a 50
Hz, three-phase source, the phase sequence being consistent
with the direction of rotation. In steady state
a) both machine act as generators
b) the dc machine acts as a generator, and the induction machine
acts as a motor
c) the dc machine acts as a motor, and the induction machine
acts as a generator
d) both machines act as motors
The synchronous speed in induction machine is
Ns = 120×50
= 1500 rpm
But the d.c motor is already driving the induction machine at
above rated speed. Hence the induction machine acts as a
generator and the dc machine acts as a motor driving induction
8. If P1 and P2 are the iron and copper losses of a transformer at
full load, and the maximum efficiency of the transformer is at
75% of the full load, then what is the ratio of P1 and P2?
= � 12
ℎ , = 75 = 3
∴ 1 = 9
9. A normal Δ - Δ connected 3-phase transformer is obtained by
connecting three single-phase transformers I, II and III as shown
If transformer III is removed, the system, would not operate in
"open-delta" mode. Under this condition, if voltage Vab is
designed by V∠600, the voltage Vca is
� ⃗ = � ⃗ + � ⃗
� ⃗ = � ⃗ + � ⃗
� ⃗ = −( � ⃗ + � ⃗ )
= −( cos 600 + cos(−600))
�∴ � � ⃗ � = � � ⃗ � = �
� ⃗ = −
� ⃗ = ∠−1800
10. When are eddy-current losses in a transformer reduced?
a) If laminations are thick
b) If the number of turns in primary winding is reduced
c) If the number of turns in secondary winding is reduced
d) If laminations are thin
Pe = KeB2f2t2 where t is thickness
11. A d.c series motor is accidentally connected to single-phase a.c
supply. The torque produced will be
a) of zero average value
c) steady and unidirectional
d) pulsating and unidirectional
In dc series motor, the ac currents through the field and armature
windings will always be in the same direction. So torque will be
unidirectional but pulsating due to ac.
12. When one transformer is removed from a Δ-Δ bank of 30 kVA
transformer, the capacity of the resulting 3-phase trans-former
corresponding input line voltages?
a) 11.5 kVA
b) 17.3 kVA
c) 20 kVA
d) 25.9 kVA
Capacity of V-V connection
= 1 × (Rating of Δ-Δ connected transformer)
= 1 × 30 = 17.3
Hence, option (b) is correct.
13. The figure given below shows a two winding core-type
transformer. The instantaneous directions of the primary current
I1, the mutual flux ϕm and the primary leakage flux ϕ1, are as
indicated in the figure; the corresponding directions, at the same
instant, of the secondary current I2, and the secondary leakage
flux Q, would be
a) I2, a to b; and ϕ2, c to d
b) I2, b to a; and ϕ2, c to d
c) I2, a to b; and ϕ2, d to c
d) I2, b to a; and ϕ2, d to c
• Direction of current I2 will be such that it produces a flux that
opposes the flux ϕm. So I2 flows from b to a.
• Leakage flux will only link with secondary but not with
primary. Leakage flux is from c to d.
14. It facilities supply of single-phase loads. Consider the
following statements concerning the utility of mesh-connected
tertiary windings in star-star transformers
1. It is used to suppress harmonic voltages.
2. It is used to allow flow of earth fault current for operation of
3. It facilities supply of single-phase loads.
4. It provides low-reactances paths for zero sequence currents.
Which of these statements are correct?
a) 1, 2, 3 and 4
b) 1, 2 and 3 only
c) 1, 2 and 4 only
d) 3 and 4 only
15. In a d.c compound generator, "flat-compound" characteristic,
required for certain applications, may be obtained by connecting
a variable resistance:
a) Across the series field
b) In series with the series field
c) In parallel with the shunt field
d) In series with the shunt field
Variable resistance in parallel with the series field winding is
16. A 3-phase synchronous generator is to be connected to the
infinite bus. The lamps are connected as shown in figure for the
synchronization. The phase sequence of bus voltage is R-Y-B
and that of incoming generator voltage is R'-Y'-B'.
It was found that the lamps are becoming dark in the sequence
La - Lb - Lc. It means that the phase sequence of incoming
a) opposite to infinite bus and its frequency is more than infinite
b) opposite to infinite bus but its frequency is less than infinite
c) same as infinite bus and its frequency is more than infinite
d) same as infinite bus and its frequency is less than infinite bus.
(i) The circuit used for synchronization is shown in fig.1.
Various voltages are shown in this figure with their
reference polarities. This information is essential for a
proper understanding of lamp behavior.
(ii) About rotation of the voltage phasors: From the theory of
representation of sinusoidal quantities by phasors all these
phasors are rotating phasors, rotating in acw direction with
peed depending on frequency.
The machine side phase voltage phasors � , � and �
rotate in the acw direction at 2πf rad/s. Since they rotate in
the same direction at the same speed, they are stationary wrt
each other. If we are considering only these phasors, we can
ignore their rotation.
The phasors � ′ , � ′ and � 1 represent voltages at fr Hz;
and so they rotate in acw direction at 2πfr r/s. Unless f = fr;
they rotate at a different speed with respect to � , � and
� phasors. It is this rotation at different speeds which
causes the observed lamp behavior.
(iii) Lamp voltages: By KVL (in fig.1),
� = � − � ′
� = � − � ′
� = � − � ′
(iv) fr > f: Machine set of phasors rotate faster. It is assumed
that supply set of phasors remain stationary while machines
set of phasors rotates anti clockwise with speed (fr – f).
(v) Machine phase-sequence R’Y’B’, fr > f: In figs.2(a), 2(b),
and 2(c), all the voltage phasors are shown at different
times. The symbol � , common to all the voltages, is omitted
(vi) Machine phase-sequence R’B’Y’, fr > f: The phasors are
again shown, at different instants of time, in fig.3.
This shows that lamps L1, L2 and L3 are becoming dark in
sequence. Hence phase sequence of incoming generator is
opposite to that of the infinite bus and frequency is more than
that of the incoming bus.
17. A separately excited DC generator has an armature resistance
of 0.1Ω and negligible armature inductance. At rated field
current and rated rotor speed, its open circuit voltage is 200 V.
When this generator is operated at half the rated speed, with half
the rated field current, an uncharged 1000μF capacitor is
suddenly connected across the armature terminals. Assume that
the speed remains unchanged during the transient.
At what time (in microsecond) after the capacitor is connected
will the voltage across it reach 25 V?
At half the rated field current and half the rated speed, induced
emf in the armature = 200 = 50
−50 + (0.1) + = 0
(0.1) + = 50
(0.1) + = 50
1000 × 10−6 � � 0.1 + = 50
10−4 + = 50
+ 104 = 50 × 104
Apply Laplace Transform on both sides
( ) + 104 ( ) = 50×104
( ) = 50×104
1 = +
( +104) +104
= 1 , = 1
( ) = 50×104 �1 + ( +1104)�
( ) = 50 − 50 −104
= 25 , =?
25 = 50 − 50 −104
50 −104 = 25
−104 = ln 0.5
= −(ln 0.5)10−4 = 6.93 × 10−5 = 69.3
18. For obtaining very quick braking of a 3-ϕ, wound-rotor
induction motor running on load.
a) a large external resistance has to be inserted in the rotor-
b) a large external resistance has to be inserted in the stator-
c) interchange any two terminals of the stator supply.
d) interchange any two terminals of the rotor to the slip-rings.
For quick braking interchange any two terminals of the stator
19. A 25 kVA, 2300/230 V 50 Hz, single-phase transformer
supplies rated load at 230 V. The ratio of its leakage reactance
to resistance is √3. The terminal voltage on reducing the load to
zero is observed to be the same as at rated load. What is the
power factor of the rated load?
b) 0.866 lagging
c) 0.866 leading
d) Zero leading
Terminal voltage at no load = Terminal voltage at rated load
Voltage regulation = 0
. = ∈ cos ∅ +∈ sin ∅
Given, ∈ = √3
∈ cos ∅ = −∈ sin ∅
− ∈ = cos ∅
tan ∅ = − ∈
= − 1
⇒ ∅ = −300
cos ∅ = 0.866 ( )
20. Match List-I (Name of test) with List-II (Result) and select
the correct answer:
A. Open circuit and short circuit tests
B. Open circuit and zero power factor tests
C. Slip test
D. Maximum lagging current test
1. Leakage reactance.
2. Direct axis synchronous reactance.
3. Quadrature axis synchronous reactance.
4. Ratio of direct axis synchronous reactance to quadrature axis
a) 1 2 4 3
b) 1 2 3 4
c) 2 1 4 3
d) 2 1 3 4
21. Match List-I (DC machine quantity) with List-II (Relation)
and select the correct answer using the code given below the
A. Developed power 1. ∝
B. Torque 2. ∝
C. Generated e.m.f
D. Speed 3. ∝
a) 2 4 1 3
b) 3 1 4 2
c) 2 1 4 3
d) 3 4 1 2
Power developed = ×
Torque ‘T’ = ∅
Back EMF ‘ ’ = ∅ hence speed ∝
22. Two transformers of different kVA ratings working in parallel
share the load in proportion to their ratings when their
a) per unit leakage impedances on the same kVA base are the
b) per unit leakage impedances on their respective ratings are
c) ohmic values of the leakage impedances are inversely
proportional to their ratings.
d) ohmic values of the leakage magnetizing reactances are the
Let transformers T1 and T2 have the same voltage ratings (V/E)
but different VA ratings S1 and S2 respectively. Let their leakage
impedances (ref sec) be 1̅ Ω and 2̅ Ω respectively. When
operating in parallel, the secondary circuit will be as shown.
� − 1̅ 1̅ = � − 2̅ 2̅ = � , from which 1̅ = � 2 and 1 = 21. If
2̅ � 1 2
(S1/S2) = (Z2/Z1) and they share a load in proportion to their
Thus the condition for the transformers to share a load in
proportion to their VA ratings is for the ohmic values of their
impedances to be inversely proportional to their ratings. (c) is
Again, consider the equation I1Z1 = I2Z2 where currents are in
amp and impedances in ohms. Let Z1 pu and Z2 pu be the pu
values based on their respective ratings.
1( ℎ ) = 1 2
2( ℎ ) = 2 2
∴ 1 1 2 = 2 2 2
If 1 = 2 ; 1 = 12, and they share the load in proportion to
their ratings. (b) is true.
23. Statement (I): The direct on-line (DOL) starter is used to start
a small dc motor.
Statement (II): DOL starter limits initial current drawn by the
a) Both Statement (I) and Statement (II) are individually true
and Statement (II) is the correct explanation of Statement (I).
b) Both Statement(I) and Statement (II) are individually true but
Statement (II) is not the correct explanation of Statement (I).
c) Statement (I) is true but Statement (II) is false.
d) Statement (I) is false but Statement (II) is true.
24. Assertion (A): The short circuit ratio (SCR) of a three-phase
alternator should be high.
Reason (R): A high value of SCR will decrease the value of
voltage regulation and will increase the maximum power output.
a) Both A and B are true and R is the correct explanation of A
b) Both A and R are true but R is NOT the correct explanation
c) A is true but R is false
d) A is false but R is true
∵ ∝ 1 . = − × 100%
For high value of SCR - should be low then V.R. would be
low and would be high.
25. When core material of resistivity 0.1×10-6Ω-m is used in a
transformer, eddy current loss is 100 W. What is the eddy
current loss in the same transformer, if the core material
resistivity is 0.4×10-6Ω-m?
a) 1600 W
b) 400 W
c) 25 W
d) 2.5 W
Eddy current loss, ∝ 2 2 3ℎ
So, ∝ 1
1 = 2 = 0.4×10−6
2 1 0.1×10−6
100 = 4 ⇒ 2 = 25
26. Match List-I (Equivalent circuit parameter) with List-II
(Values) for a 50 MVA three phase alternator and select the
A. Armature resistance 1. 1 p.u
B. Synchronous reactance 2. 0.1 p.u
C. Leakage reactance 3. 0.01 p.u
a) 1 2 3
b) 3 1 2
c) 3 2 1
d) 1 3 2
27. Assertion (A): In a certain case, a d.c shunt generator failed to
build up the voltage.
Reason (R): Shunt field resistance of a d.c shunt generator
should be more than its critical field resistance value to generate
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
c) A is true but R is false.
d) A is false but R is true.
If shunt field resistance is more than the critical field resistance,
there will be no voltage build up.
28. The efficiency of a 100 kVA transformer is 0.98 at full as well
as at half load. For this transformer at full load the copper loss
a) is less than core loss.
b) is equal to core loss.
c) is more than core loss
d) none of the above
Efficiency = × .
× . + +
Let P.f = unity,
= 100 ×1 … ( )
100 ×1+ + … ( )
ℎ = 50 ×1
50 ×1+ +41
Solving (1) & (2) = 2
29. The figure shows the speed torque characteristics of the
following dc motors.
a) Shunt motor
b) Series motor with weak shunt field
c) Cumulatively compound motor
d) Differentially compound motor
The no-load speed of all the motor is same.
Match the type of motors with corresponding curve using the
codes given below:
a) 1 4 3 2
b) 2 3 4 1
c) 1 3 4 2
d) 2 4 3 1
4 → series motor
3 → cumulatively compound
2 → shunt motor
1 → differentially compound as ϕsh and ϕse are in opposite
30. The internal characteristic of a dc generator is plotted between
a) armature current and voltage generated after armature
b) field current and voltage generated at no load.
c) field current and voltage generated on load.
d) armature current and voltage generated at the output
Internal characteristic of a dc generator is plotted between the
armature current and voltage generated after armature reaction.