The starting torque of an induction motor is _______ when rotor resistance equals rotor reactance.

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Question

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ALP CBT 2 Electrician Previous Paper: Held on 22 Jan 2019 Shift 2

Answer 1

Torque equation:

The torque equation of a three-phase induction motor is given by,

\(T = \frac{{180}}{{2\pi {N_s}}}\left( {\frac{{sV^2{R_2}}}{{\left( {R_2^2 + {s^2}X_2^2} \right)}}} \right)\)

Where Ns is the synchronous speed

V = supply voltage

R2 = rotor resistance

X2 = rotor reactance

s is the slip

By the above expression, we can say that the torque of an induction motor depends on rotor resistance and slip.

Condition for maximum torque:

The condition to get the maximum torque at starting is,

\({s_m} = \frac{{{R_m}}}{{{X_m}}} = 1\)

Xm = Rm

Where,

Rm = Motor resistance per phase

Xm = Motor reactance per phase

At the starting of the three-phase slip ring induction motor

Slip (s) = 1 (At the starting N_r = 0)

Therefore, \({s_m} = \frac{{{R_m}}}{{{X_m}}} = 1\)

⇒ X_m = R_m

Hence the starting torque of an induction motor is maximum when rotor resistance equals rotor reactance.