AC Machines Part 2

(Induction Motors)
Prepared by: Engr. David DC. Flores

1. At a location in Europe, it is necessary to supply 300 kW of 60 Hz power. The only power sources
available operate at 50 Hz. It is decided to generate the power by means of a motor-generator
set consisting of a synchronous motor driving a synchronous generator. How many poles should
each of the two machines have in order to convert 50 Hz power to 60 Hz power?
a. 12 and 14 b. 14 and 16 c. 8 and 10 d. 10 and 12
2. A 60 Hz, 4 pole, 3 phase induction motor has a slip of 2.5%. What is the slip speed in rpm?
a. 55 b. 40 c. 60 d. 45
3. An induction motor runs at 1,150 rpm. What is the frequency of the rotor emf in Hz?
a. 1.8 Hz b. 4 Hz c. 3 Hz d. 2.5 Hz
4. The nameplate speed of a 60Hz, 6 pole, 3 phase induction motor is 1,164 rpm. Find its percent
speed regulation if its no-load speed is 1,188 rpm.
a. 4.22% b. 1.86% c. 2.06% d. 3.24%
5. A squirrel cage induction motor with nameplate data of 150 Hp, 3 phase, 460 V, 60 Hz, 6 poles,
0.85 pf was subjected to a certain performance test. The test result readings were as follows: Full
load current = 194 A and full load torque = 918 N-m. Find the percent full load slip.
a. 3% b. 2% c. 4% d. 5%
6. A 480 V, 60 Hz, six-pole three-phase synchronous motor draws 80 A from the line at unity power
factor and full load. If the motor is lossless, what is the output torque of this motor?
a. 568 N-m b. 597 N-m c. 542 N-m d. 529 N-m
7. Referring to problem 6, what will be the magnitude of the line current if the power factor is
adjusted to 0.8 leading?
a. 98 A b. 100 A c. 102 A d. 104 A
8. A 480 V, 60 Hz, 400 Hp 0.8 pf leading eight-pole ∆ connected synchronous motor has a
synchronous reactance of 1.0 Ω and negligible armature resistance. Ignore its friction, windage
and core losses for this purpose. If this motor is initially supplying 400 Hp at 0.8 pf lagging, what
are the magnitudes and angles of EA ?
a. 358∠ − 23.6° b. 358∠ − 32.6° c. 385∠ − 32.6° d. 385∠ − 23.6°
9. A 10 Hp, 230 V, 60 Hz, 6 pole, wye-connected 3 phase induction motor has the following per
phase parameters referred to the stator: r1 = 0.3 ohm, X1 = 0.5 ohm, r2 = 0.15 ohm, X2 = 0.2 ohm,
X0 = 12.5 ohms, R0 = 350 ohms. Find the power developed y the motor in watts at a slip of 3%.
a. 8,353 W b. 8,185 W c. 7,625 d. 7,890
10. A 7.5 Hp, 230 V, 60 Hz, 4 pole, wye-connected 3 phase induction motor has the ff per phase
parameters, r1 = r2 = 0.24 ohm, X1 = X2 = 0.48 ohm, X0 = 15 omhs, R0 = 300 ohms. The motor
develops full load torque at a slip of 3%. Find the roto input power in watts. Use the approximate
equivalent circuit diagram of the motor.
a. 5,635 W b. 6,144 W c. 6,310 W d. 5,983 W
11. Referring to problem no. 10, find the percent efficiency of the motor at full load.
a. 88.2% b. 85% c. 87% d. 86%
12. Referring to problem no. 10, find the line current in amperes and the percent power factor at full
load.
a. 19.52, 83.64 b. 19.52, 88.5 c. 21.5, 83.64 d. 21.5, 88.5
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13. A 230 V, 4 pole, 60 Hz, 3 phase, wye-connected induction motor has rotor resistance and
standstill leakage reactance of 0.1 and 0.9 ohm/phase, respectively. The turns phase ratio is 2:1.
If the full load slip 4.5%, find the gross torque at full load in N-m.
a. 25 b. 31 c. 27 d. 29

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14. A 3-phase induction motor has rotor resistance and standstill leakage reactance of 0.1 ohm and
3.5 ohms phase, respectively. The rotor emf at standstill is 60 V/ phase. For an slip of 5%, what
is the power developed in watts?
a. 1,355 W b. 1,623 c. 1,362 d. 1,263
15. The rotor of a 3-phase, 60 Hz, 4 pole induction motor takes 120 kW at 3 Hz. Find the rotor copper
loss in kW.
a. 6 kW b. 4 kW c. 8 kW d. 9 kW
16. The eddy current loss in an ac motor is 100 watts at 50 Hz. Its loss at 100 Hz will be,
a. 25 W b. 59 W c. 100 W d. 400 W
17. A 60 z, 4-pole, 3 phase wound-rotor induction motor has rotor resistance and standstill leakage
reactance of 0.1 and 0.8 ohm/phase, respectively. How much additional resistance must be
inserted in the rotor in ohms/phase so that the motor has maximum starting torque?
a. 0.6 Ω b. 0.7 Ω c. 0.06 Ω d. 0.07 Ω
18. Calculate the rotor resistance per phase in ohms of a 6 pole, 60 Hz, 3-phase induction motor if
the motor develops a maximum torque of 300 N-m at 780 rpm. The rotor leakage reactance at
standstill is 3 Ω/phase.
a. 1.05 Ω b. 0.05 Ω c. 1.07 Ω d. 1.02 Ω
19. A 440 V, 60 Hz, 6 pole, 3-phase induction motor has rotor input power of 33 kW at rated voltage
and frequency. Under this condition, the rotor emf makes 126 complete cycles/minute. Find the
rotor resistance in ohm/phase if the rotor current is 60 A/ phase.
a. 0.0118 Ω b. 0.0107 Ω c. 0.107 Ω d. 0.118 Ω
20. A 15 Hp, 400 V, 3-phase, Y-connected synchronous motor has full load efficiency of 90%. The
synchronous reactance is 3 ohms/phase. If the motor operates at full load at 0.8 pf leading, find
the torque angle in electrical degrees.
a. -13.7⁰ b. -14.7⁰ c. -11.2⁰ d. -12.7⁰
21. If the maximum torque developed by a 3 phase induction motor is 100 N-m at an slip of 12%,
what is the torque developed at 6% slip in N-m?
a. 90 N-m b. 80 N-m c. 75 N-m d. 85 N-m
22. A 3,300 V, 24 pole, 60 Hz, 3 phase wye-connected induction motor has rotor resistance and
standstill leakage reactance of 0.016 and 0.265 ohm/phase, respectively. Calculate the ratio of
the full load torque to the maximum torque developed if full load speed Is 296.4 rpm.
a. 0.25 b. 0.415 c. 0.382 d. 0.585
23. The starting torque of a 7.5 Hp, 460 V, 1,730 rpm, 3 phase induction motor is 2.5 times the full
load value. Find the starting torque in N-m if the voltage is reduced to 230 V.
a. 19.3 N-m b. 21.6 N-m c. 33.2 N-m d. 26.9 N-m
24. An induction motor while driving a load takes 350 kW at 0.707 pf lagging. An over-excited
synchronous motor is then connected in parallel with the induction motor taking 150 kW of power.
If the combined power factor becomes 0.9 lagging, calculate the kVA rating of the synchronous
motor.
a. 178.5 kVA b. 245.2 kVA c. 185.4 kVA d. 184.75 kVA
25. A motor is used with respective load at given time. Find the hp rating of the motor.
Load (kW) 20 40 80 60 0
Time (min) 10 10 10 5 10
a. 6 kW b. 64 kW c. 7 kW d. 67 kW
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