What happens to the torque and power output of a variable-torque motor when the speed doubles?

In a variable-torque motor, the relationship between torque and speed is key to understanding how power output is affected when speed changes. The power output of a motor can be calculated with the formula: Power = Torque × Speed.

When the speed of the motor doubles, the torque in a variable-torque application does not necessarily remain constant. In fact, for many types of motors, particularly those in applications like fans and pumps, torque will generally vary with speed.

If torque doubles when speed doubles, we can analyze the power output using the power formula again: if both torque and speed are doubled, the new power output would be:

New Power = (2 × Torque) × (2 × Speed) = 4 × Torque × Speed

This shows that the power output quadruples under the condition that torque doubles with the increase in speed. Hence, the relationship of torque to speed for a variable-torque motor indicates that if the torque does indeed double as the speed doubles, it logically follows that the power will quadruple as well.

This understanding clarifies why the correct answer is that torque doubles while the power output quadruples when the speed doubles, reflecting the fundamental operational principles of variable-torque motors.