Explanation:

When the supply voltage of an induction motor is doubled, the torque produced by the motor will increase by a factor of four. This can be explained by understanding the relationship between voltage, current, and torque in an induction motor.

1. Voltage and Current:
In an induction motor, the stator windings are connected to the power supply, and the rotor windings create a rotating magnetic field. The stator windings are designed to operate at a specific voltage, which determines the current flowing through the windings.

When the supply voltage is doubled, the current flowing through the windings also doubles (according to Ohm's law, V=IR). This increased current results in a stronger magnetic field in the stator, which interacts with the rotor to produce torque.

2. Torque and Current:
The torque produced by an induction motor is directly proportional to the current flowing through the windings. This is because the magnetic field generated by the stator windings interacts with the rotor to create a torque force.

When the current is doubled, the torque produced by the motor also doubles. This is because the increased current creates a stronger magnetic field, resulting in a greater torque force.

3. Torque and Voltage:
The torque produced by an induction motor is also directly proportional to the square of the voltage applied to the stator windings. This relationship is known as the torque equation:

T ∝ V^2

This means that when the voltage is doubled, the torque produced by the motor will increase by a factor of four (2^2 = 4). Similarly, if the voltage is halved, the torque will decrease by a factor of four.

Conclusion:
In summary, when the supply voltage of an induction motor is doubled, the torque produced by the motor will be four times greater. This is because the increased voltage results in a higher current flowing through the windings, which in turn creates a stronger magnetic field and a greater torque force.