The maximum torque of a 3-phase induction motor under running conditions is

From the below diagram we can observe that the maximum torque of an induction motor is independent of rotor resistance but slip at which maximum torque occurs depends on rotor resistance and they change on adding the additional resistance to the rotor circuit.

The maximum torque of an induction motor is given by

\({T_{max}} = \frac{{kE_{20}^2}}{{2{X_{20}}}}\)

∴ Maximum torque is directly proportional to supply voltage & maximum torque is inversely proportional to rotor reactance.

Hence, the maximum torque is dependent on the supply voltage & reactance of the rotor and is independent of the rotor resistance.

Sm the value of slip corresponding to the maximum torque is

\({S_m} = \frac{{{R_2}}}{{{X_{20}}}}\)

Therefore, slip at which maximum torque occurs is directly proportional to rotor resistance R2.