211.MET December 2022 Q.8(b)

 A three phase induction motor is wound for four poles and is supplied from a 50 Hz system. Calculate. i. The synchronous speed; ii. The speed of the rotor when the slip is 4 per cent; iii. The motor frequency when the speed of the rotor is 600 r.p.m

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Given 

No of poles P = 4
Frequency f = 50 Hz
Slip s = 4% = 0.04

To Find

 i. The synchronous speed
ii. The speed of the rotor when the slip is 4 per cent
iii. The motor frequency when the speed of the rotor is 600 r.p.m

Solution

i) Synchronous speed Ns = 120f / P
                                         = (120 x 50) / 4
                                         = 1500 rpm

                                slip s = (Ns - N) / Ns

ii) Rotor speed N = Ns (1 - s)
                             = 1500 (1 - 0.04)
                             = 1440 rpm

iii) Motor frequency when N = 600 rpm
                                    Slip s  =(Ns - N) / Ns
                                               = (1500 - 600) / 1500
                                               = 0.6

                   Motor frequency = slip x f
                                               = 0.6 x 50
                                               = 30 Hz