Question

A 500 HP, 440 V, 3-phase, 50 Hz induction motor runs at 950 r.p.m. when on full load with a synchronous speed of 1000 r.p.m. For this condition, the frequency of the rotor current will be
1. 4.0 Hz
2. 3.5 Hz
3. 2.5 Hz
4. 2.0 Hz

Answer 1

Correct Answer - Option 3 : 2.5 Hz

Concept:

Synchronous speed in rpm of a three-phase induction motor is given by,

\({N_s} = \frac{{120f}}{P}\)

Where f is the frequency in Hz

P is the number of poles

A rotor of a three-phase induction motor rotates at a speed close to the synchronous speed but not equal to the synchronous speed.

The difference between the synchronous speed and the rotor speed is known as slip speed. It is given by

Slip speed = Ns - Nr

Slip is defined as the ratio of slip speed to the rotor speed.

\(s = \frac{{{N_s} - {N_r}}}{{{N_s}}}\)

Frequency of rotor current = sf

Calculation:

Given that,

N = 1000 rpm, Nr = 950 rpm

Supply frequency (f) = 50 Hz

\(s = \frac{{{1000} - {950}}}{{{1000}}}\)

⇒ s = 0.05

Rotor current frequency (fr) = 0.05 x 50

fr = 2.5 Hz