The frequency of the EMF in the stator of a 4 - pole induction motor is 50 Hz and that in the rotor in 1.5 Hz. Find the speed at which the motor is running.

Concept:

The synchronous speed is given by

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

f is the frequency in Hz or C/s

P is the number of poles

The induction motor rotates at a speed (Nr) close to but less than the synchronous speed.

Slip of an induction motor is given by,

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

Where Ns is the synchronous speed

And Nr is the rotor speed

The frequency of rotor current = sf

Calculation:

Given:

f = 50 Hz

f_r = 1.5 Hz

P = 4

\(s = \frac{f}{f_r} = \frac{1.5}{50} = 0.03\)

\(N_s = \frac{120f}{P} = \frac{120\times50}{4}= 1500 ~RPM \\ N_r = (1 - s)~N_s = (1-0.03)~1500 = 1455 RPM \)