Question

A 12-pole, 3-phase, 50 Hz induction motor runs at 475 rev/min. Determine the slip speed and frequency of the rotor currents.

• A. 20 rev/min, 2.5 Hz
• B. 25 rev/min, 3.5 Hz
• C. 25 rev/min, 2.5 Hz
• D. 20 rev/min, 3.5 Hz

Hint:

Rotor current frequency in an induction motor is directly proportional to slip. At synchronous speed, rotor frequency becomes zero.

Answer 1

The Correct Option is C

Step 1: The synchronous speed is \( N_s = \frac{120f}{P} = \frac{120 \times 50}{12} = 500 \) rev/min.
Step 2: The percentage slip is \( s\% = \frac{N_s - N}{N_s} \times 100 = \frac{500 - 475}{500} \times 100 = 5\% \).
Step 3: The slip speed is \( 5\% \) of \(N_s\), i.e. \( \frac{5}{100} \times 500 = 25 \) rev/min, and the rotor current frequency is \(5\%\) of the supply frequency, i.e. \( \frac{5}{100} \times 50 = 2.5 \) Hz.
\[ \boxed{25 \text{ rev/min and } 2.5 \text{ Hz}} \]

Answer 2

The slip speed of an induction motor is the speed at which the rotor mechanically lags behind the rotating magnetic field, and the rotor current frequency is simply this same lag expressed as a fraction of the supply frequency. Since the synchronous speed here is fixed at \(N_s = \frac{120 \times 50}{12} = 500\) rev/min, the slip fraction can be found from the slip speed value quoted in each option, and this slip fraction can then be used to predict the rotor frequency that should accompany it.

1. 20 rev/min, 2.5 Hz: A slip speed of 20 rev/min gives a slip fraction of \(20/500 = 0.04\), so the rotor frequency should be \(0.04 \times 50 = 2\) Hz, not the 2.5 Hz quoted here.
2. 25 rev/min, 3.5 Hz: A slip speed of 25 rev/min gives a slip fraction of \(25/500 = 0.05\), so the rotor frequency should be \(0.05 \times 50 = 2.5\) Hz, not the 3.5 Hz quoted here.
3. 25 rev/min, 2.5 Hz: A slip speed of 25 rev/min gives a slip fraction of \(25/500 = 0.05\), so the rotor frequency should be \(0.05 \times 50 = 2.5\) Hz, which is exactly the value quoted.
4. 20 rev/min, 3.5 Hz: A slip speed of 20 rev/min gives a slip fraction of 0.04, so the rotor frequency should be 2 Hz, not the 3.5 Hz quoted here.

Working forward from the slip speed to the predicted rotor frequency, only the 25 rev/min, 2.5 Hz pair is self-consistent, since the mechanical lag of 475 rev/min out of a 500 rev/min field must translate into both figures simultaneously.

Therefore, the correct answer is 25 rev/min, 2.5 Hz.