- 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 = K _{T} s α / (s^{2} + α^{2})**

Where **K _{T}** is torque constant = 3 (E

_{1})

^{2}/ ω

_{s}X

^{’}

_{2}

And ** α** is the machine constant = R^{’}_{2} / X^{’}_{2}

- Now when an external resistance is added up in series with rotor then ≫

**Value of Slip corresponding to maximum torque gets changed as R**^{’}_{2}changed.**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**s**that is equal to_{max}**α**gets shifted.

** s _{max }= ( R^{’}_{2 }+ x ) / X^{’}_{2}**

**T _{m} = K_{T} / 2 (When s = α) = 1.5 (E_{1})^{2} / ω_{s} X^{’}_{2}**

- It can be observed that
**T**is independent of_{m}**R**hence whatever may be the rotor resistance, maximum torque produced never changes but the slip and speed at which it occurs depends on^{’}_{2 }**R**^{’}_{2.}

- Due to this, we get a new torque – slip characteristics for rotor resistance (
**R**^{’}_{2 }+ x ). This new characteristics is parallel to the characteristics for with same T_{m}but occurring at different value of slip.

**It can be seen that the starting torque T**^{’}_{st}for R^{’}_{2}is more than T_{st}for ( R^{’}_{2 }+ 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) = X^{’}_{2} – R^{’}_{2}

**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 (I^{2} 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.**