Correct Answer - Option 1 : 1164 rpm
Concept:
The synchronous speed is given by
\({N_s} = \frac{{120f}}{P}\)
Where,
f is the supply frequency in Hz or C/s
P is the number of poles
The induction motor rotates at a speed (Nr) close 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
Rotor current frequency (fr) = (s)(f)
The slip is negative when the rotor speed is more than the synchronous speed of the rotor field and is in the same direction.
Calculation:
Given -
Number of poles (P) = 6
Frequency (f) = 60 Hz
\({N_s} = \frac{{120 \times 60}}{6} = 1200\;rpm\)
Slip (s) = 3 % = 0.03
Now rotor speed is
Nr = Ns (1 – s) = 1200 (1 – 0.03)
Nr = 1164 rpm
Rotor current frequency (fr) = 0.03 x 60
fr = 1.8 Hz