The maximum torque in an induction motor is developed when which two parameters are equal?

The maximum torque in an induction motor occurs when the rotor reactance equals the rotor resistance. This principle is rooted in the behavior of the motor under varying load conditions. As the load on the motor increases, the slip – which is the difference between the synchronous speed of the magnetic field and the actual speed of the rotor – also increases, affecting the rotor's current and consequently its reactance and resistance.

When the rotor reactance and resistance are equal, the power factor is at its maximum, and this balance optimizes the current induced in the rotor, leading to the highest torque generation. This scenario, known as the "maximum torque condition", ensures that the motor operates efficiently under varying loads, which is critical for applications requiring reliable starting and acceleration characteristics.

In contrast, other parameters such as voltage and current, stator and rotor speeds, or the relationship between torque and power do not directly determine the maximum torque condition in induction motors. For instance, the stator speed is constant given the synchronous speed, and while torque and power are related, their equality does not signify maximum torque. Therefore, recognizing the specific relationship between rotor reactance and resistance is key to understanding the generation of maximum torque in induction motors.