Question

A 4-pole, 3-phase induction motor operates from a supply whose frequency is 60 Hz. calculate: 1- the speed at which the magnetic field of the stator is rotating

Answer 1

Answer:

The answer is below

Explanation:

A 4-pole, 3-phase induction motor operates from a supply whose frequency is 60 Hz. calculate: 1- the speed at which the magnetic field of the stator is rotating. 2- the speed of the rotor when the slip is 0.05. 3- the frequency of the rotor currents when the slip is 0.04. 4- the frequency of the rotor currents at standstill.

Given that:

number of poles (p) = 4, frequency (f) = 60 Hz

1) The synchronous speed of the motor is the speed at which the magnetic field of the stator is rotating. It is given as:

$n_s=\frac{120f}{p}=\frac{120*60}{4}=1800\ rpm$

2) The slip (s) = 0.05

The speed of the motor (n) is the speed of the rotor, it is given as:

$n=n_s-sn_s\\\\n=1800-0.05(1800)\\\\n=1800-90\\\\n=1710\ rpm$

3) s = 0.04

The rotor frequency is the product of the supply frequency and slip it is given as:

$f_r=sf\\\\f_r=0.04*60\\\\f_r=2.4\ Hz$

4) At standstill, the motor speed is zero hence the slip = 1:

$s=\frac{n_s-n}{n_s}\\ \\n=0\\\\s=\frac{n_s-0}{n_s}\\\\s=1$

The rotor frequency is the product of the supply frequency and slip it is given as:

$f_r=sf\\\\f_r=1*60\\\\f_r=60\ Hz$