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: Calculate the synchronous speed of the motor.
Synchronous speed is given by
\[ N_s = \frac{120 f}{P} \]
\[ N_s = \frac{120 \times 50}{12} = 500 \text{ rev/min} \]
Step 2: Calculate the slip speed.
\[ \text{Slip speed} = N_s - N \]
\[ \text{Slip speed} = 500 - 475 = 25 \text{ rev/min} \]
Step 3: Calculate the slip of the motor.
\[ s = \frac{N_s - N}{N_s} = \frac{25}{500} = 0.05 \]
Step 4: Calculate the rotor current frequency.
Rotor current frequency is given by
\[ f_r = s f \]
\[ f_r = 0.05 \times 50 = 2.5 \text{ Hz} \]
Step 5: Conclusion.
The slip speed and rotor current frequency are
\[ \boxed{25 \text{ rev/min and } 2.5 \text{ Hz}} \]

Answer 2

This question asks for the slip speed and the rotor current frequency of a 12-pole, 3-phase, 50 Hz induction motor running at 475 rev/min. Instead of computing the slip speed and rotor frequency separately, each option can be checked for internal consistency using the relationship between slip speed and rotor frequency, since both quantities are tied to the same slip value.

The synchronous speed of the rotating field is fixed by the supply frequency and the number of poles: \[ N_s = \frac{120 f}{P} = \frac{120 \times 50}{12} = 500 \text{ rev/min} \] For any slip \(s\), the slip speed equals \(sN_s\) and the rotor current frequency equals \(sf\). So the slip fraction implied by the rotor frequency in each option must reproduce the same slip fraction implied by the slip speed in that option, or the option is inconsistent.

1. 20 rev/min, 2.5 Hz: A rotor frequency of 2.5 Hz implies \(s = 2.5/50 = 0.05\), which requires a slip speed of \(0.05 \times 500 = 25\) rev/min, not 20 rev/min. The two figures do not correspond to the same slip, so this option is inconsistent.
2. 25 rev/min, 3.5 Hz: A rotor frequency of 3.5 Hz implies \(s = 3.5/50 = 0.07\), which requires a slip speed of \(0.07 \times 500 = 35\) rev/min, not 25 rev/min. Inconsistent.
3. 25 rev/min, 2.5 Hz: A rotor frequency of 2.5 Hz implies \(s = 2.5/50 = 0.05\), which requires a slip speed of \(0.05 \times 500 = 25\) rev/min. This matches the stated slip speed exactly, so both figures correspond to the same slip fraction.
4. 20 rev/min, 3.5 Hz: A rotor frequency of 3.5 Hz implies \(s = 0.07\), which requires a slip speed of 35 rev/min, not 20 rev/min. Inconsistent.

Only the pair of values in which the slip speed and the rotor frequency arise from the same slip fraction can be physically valid together, and that happens for 25 rev/min and 2.5 Hz.

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