Question

A balanced three-phase, 50 Hz voltage is applied to a 3 phase, 4 pole, induction motor. When the motor is delivering rated output, the slip is found to be 0.05. The speed of the rotor m.m.f. relative to the rotor, structure is
1. 1500 r.p.m
2. 1425 r.p.m
3. 25 r.p.m
4. 75 r.p.m

Answer 1

Correct Answer - Option 4 : 75 r.p.m

Concept:

In a 3-phase induction motor, the synchronous speed & slip can be calculated as

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

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

Nr = Ns (1 – s) 

Where, Ns = Synchronous speed in rpm,

Nr = Rotor speed in rpm,

s = Slip of the machine,

f = Supply frequency in Hz,

P = Number of poles,

The speed of the rotor m.m.f. relative to the rotor, structure = N_s - N_r

Calculation:

Given

f = 50 Hz

P = 4

s = 0.05

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

\({N_s} = \;\frac{{120\times50}}{4}=1500\) rpm

Nr = Ns (1 – s)

N_r = 1500 (1 – 0.05)

N_r = 1425 rpm

The speed of the rotor m.m.f. relative to the rotor, structure = 1500 - 1425

= 75 rpm