Solution Electrical Numerical 1

Numerical 1: A 4-pole, 3-phase induction motor operates from a supply whose frequency is 50 Hz. Calculate (i) Speed at which the magnetic field of the stator is rotating, (ii) speed of the rotor when the slip is 0.04, (iii) the frequency of the rotor current when the slip is 0.03.

Solution: f = 50Hz

P = 4

(i) The synchronous speed 

$\displaystyle \mathrm{N_S = \frac{120\times f}{p}}$

$\displaystyle \displaystyle \mathrm{N_S = \frac{120\times 50}{4}= 1500 RPM}$ 

(ii) speed of the rotor when the slip is 0.04

Slip, $\displaystyle \displaystyle \mathrm{S = \frac{N_s - N_r}{N_s}}$ 

$\displaystyle \displaystyle \mathrm{0.04 = \frac{1500 - N_r}{1500}}$ 

Thus, Rotor speed $\displaystyle \displaystyle \mathrm{N_r = 1440}$ 

(iii) the frequency of the rotor current when the slip is 0.03

$\displaystyle \displaystyle \displaystyle \mathrm{f' = s\times f\ =\ 0.03\times 50 \ =\ 1.5\, Hz }$