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Induction motors: board exam questions with solutions

On the REE exam under Electrical Engineering Professional Subjects and the RME exam under Technical Subjects. Try each question before you open its solution, then practise with fresh numbers below: 3 computed question types on this topic.

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Questions

1. What is the synchronous speed of a 4-pole induction motor on a 60 Hz supply?

  1. 1800 rpm
  2. 3600 rpm
  3. 1500 rpm
  4. 1200 rpm
Show the answer and solution

Answer: A. 1800 rpm

Ns = 120 f/P = 120 × 60/4 = 1800 rpm.

2. A 6-pole, 60 Hz induction motor runs at 1164 rpm. What is its slip?

  1. 3.1%
  2. 3.0%
  3. 36.0%
  4. 35.3%
Show the answer and solution

Answer: B. 3.0%

Ns = 120 × 60/6 = 1200 rpm. s = (1200 − 1164)/1200 = 0.030 = 3.0%.

3. An induction motor on a 60 Hz supply runs at 3% slip. What is the frequency of the rotor currents?

  1. 58.2 Hz
  2. 60 Hz
  3. 1.8 Hz
  4. 0.03 Hz
Show the answer and solution

Answer: C. 1.8 Hz

Rotor frequency f_r = s × f = 0.03 × 60 = 1.8 Hz.

4. The air-gap power of a three-phase induction motor is 20 kW and the slip is 4%. What is the gross mechanical power developed (before friction and windage losses)?

  1. 20.8 kW
  2. 0.8 kW
  3. 20.0 kW
  4. 19.2 kW
Show the answer and solution

Answer: D. 19.2 kW

Rotor copper loss = s × P_ag = 0.04 × 20 = 0.8 kW. Developed mechanical power = (1 − s) P_ag = 20 − 0.8 = 19.2 kW.

5. A 15 kW, 400 V three-phase induction motor has 90% efficiency and 0.85 power factor at full load. What line current does it draw?

  1. 28.3 A
  2. 25.5 A
  3. 49.0 A
  4. 24.1 A
Show the answer and solution

Answer: A. 28.3 A

Input = 15 000/0.9 = 16667 W. I = P_in/(√3 V pf) = 16667/(1.732 × 400 × 0.85) = 28.3 A.

6. How is the direction of rotation of a three-phase induction motor reversed?

  1. Interchange all three supply lines in rotation
  2. Interchange any two of the three supply lines
  3. Reverse the polarity of the rotor winding
  4. Reduce the supply frequency
Show the answer and solution

Answer: B. Interchange any two of the three supply lines

Swapping any two lines reverses the phase sequence, which reverses the rotating magnetic field and hence the rotor direction.

7. The starting torque of an induction motor is proportional to the square of the applied voltage. If the starting voltage is reduced to 80% of rated, the starting torque becomes what percentage of its full-voltage value?

  1. 80%
  2. 89%
  3. 64%
  4. 51%
Show the answer and solution

Answer: C. 64%

T ∝ V², so T = 0.8² = 0.64 = 64% of the full-voltage starting torque.

8. A 4-pole, 60 Hz induction motor has rotor resistance 0.4 Ω and standstill rotor reactance 2.0 Ω per phase (referred values; stator impedance neglected). At what speed does maximum torque occur?

  1. 1800 rpm
  2. 360 rpm
  3. 1500 rpm
  4. 1440 rpm
Show the answer and solution

Answer: D. 1440 rpm

Maximum torque occurs at slip s = R2/X2 = 0.4/2.0 = 0.2. Ns = 1800 rpm, so N = 1800 × (1 − 0.2) = 1440 rpm.

Worked examples with computed numbers

These numbers are fixed on this page; in practice they change every time.

9. A 6-pole, 60 Hz induction motor runs at 5% slip. What is its speed?

  1. 570 rpm
  2. 1200 rpm
  3. 60 rpm
  4. 1140 rpm
Show the answer and solution

Answer: D. 1140 rpm

ns = 120f/P = 120 × 60/6 = 1200 rpm; n = ns(1 − s) = 1140 rpm.

10. A 4-pole, 60 Hz induction motor runs at 1720 rpm. What is its slip?

  1. 95.6%
  2. 4.65%
  3. 4.44%
  4. 0.8%
Show the answer and solution

Answer: C. 4.44%

ns = 7200/4 = 1800 rpm; s = (ns − n)/ns = 80/1800 = 4.44%.

11. A 10 hp single-phase motor runs at full load from 220 V with 80% efficiency and 0.85 pf. What current does it draw?

  1. 49.9 A
  2. 33.9 A
  3. 39.9 A
  4. 66.8 A
Show the answer and solution

Answer: A. 49.9 A

Input = output/η: I = hp × 746/(V·η·pf) = 7460/(220 × 0.8 × 0.85) = 49.9 A.

Other topics in the same subjects

DC circuits · AC circuits · Three-phase systems · Transients (RC, RL, RLC) · Semiconductors and diodes · Power electronics · Instrumentation and measurement · Control systems · Transformers · DC machines · Synchronous machines · Power systems and transmission · Protection: fuses, breakers, relays · Illumination · Power plant engineering · PEC: branch circuits, ampacity and protection · Tools and test equipment · Motors, starters and control circuits · RA 7920 and ethics (electrical)

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