When maximum starting torque is obtained in an induction motor, than rotor power will be-

Maximum Starting Torque in Induction Motors:

In an induction motor, the maximum starting torque (also known as the "breakdown torque" or "pull-out torque") is the highest torque that the motor can produce under starting conditions. This occurs when the slip (s) is such that the rotor resistance is equal to the rotor reactance. At this point, the power factor of the rotor circuit is 0.707 lagging.

Here's a detailed explanation of the concept:

• In an induction motor, torque (T) is a function of slip (s). The torque produced by the induction motor is given by the formula:

  

  where \( R_2 \) is the rotor resistance and \( X_2 \) is the rotor reactance.
• As the slip increases from zero, the torque increases until it reaches a maximum value (maximum torque) and then starts to decrease.
• The condition for maximum torque can be derived by differentiating the torque equation with respect to slip (s) and setting the derivative to zero. This gives the condition for maximum torque as:

  

• At this point, the rotor impedance is minimum and the rotor current is at its maximum value. The rotor power factor at this condition is:

  

• Therefore, at the maximum starting torque, the rotor power factor is 0.707 lagging.

Hence, the correct answer is option 3 (0.707 Lagging).