# Effect of Change in Rotor Resistance on Torque

• It is known that in slip ring induction motor, externally resistance can be added in the rotor.

Let us see the effect of change in rotor resistance on the torque produced.

We know that torque produced by an induction motor is given by

T = KT s α / (s2 + α2)

Where KT is torque constant = 3 (E1)2 / ωs X2

And α is the machine constant = R2 / X2

• Now when an external resistance is added up in series with rotor then ≫
1. Value of Slip corresponding to maximum torque gets changed as R2 changed.
2. Maximum torque remains unaltered.

• Let ‘x’ is the per phase value of inserted resistance in series with rotor then ≫

•   Machine constant α gets changed or increased to a new value. Hence value of slip corresponding to maximum torque smax that is equal to  α  gets shifted.

smax = ( R2 + x ) / X2

Tm = KT / 2 (When s = α) = 1.5 (E1)2 / ωs X2

• It can be observed that Tm is independent of R hence whatever may be the rotor resistance, maximum torque produced never changes but the slip and speed at which it occurs depends on R2.

• Due to this, we get a new torque – slip characteristics for rotor resistance ( R2 + x ). This new characteristics is parallel to the characteristics for with same Tm but occurring at different value of slip.

• It can be seen that the starting torque Tst for R2 is more than Tst for ( R2 + x ) . Thus by changing rotor resistance the starting torque can be controlled.

• If now resistance is further added to rotor ( So upto what extent it can be increased ?)

See the Torque – Slip characteristics when rotor resistance is varying.

Rotor resistance can be increased upto that when Starting torque becomes equal to Maximum value of torque, because after that Starting torque gets reduced. This value of resistance is called Critical Resistance.

When slip at starting becomes equal to slip corresponding to maximum torque.

Value of Critical Resistance (x) = X2 – R2

Thus by adding external resistance to rotor till it becomes equal to, the maximum torque can be achieved at start.

If such a high resistance is kept permanently in the circuit, there will be large copper losses (I2 R) and hence efficiency of the motor will be very poor. Hence such added resistance is cut-off gradually and finally removed from the rotor circuit, in the normal running condition of the motor. So this method is used in practice to  achieve higher starting torque hence resistance in rotor is added only at start.