Hi Brayden Noh

not generally. The speed / force dependence of the load is the crucial part. Examples:

a) lifting a weight (force nearly indenpent of (low) speed),

b) driving a fast vehicle on a horizontal plane (force about proportional to the square of the speed, due to air resistance).

In the simplest case, the motor consists of permanentmagnets and electromagnets; here the force generated by the motor is roughly proportional to the current, and the voltage Vgen generated by the motor (in opposite direction to the voltage Vext applied externally) is proportional to the speed. Usually, the difference Vext - Vgen is considerably less than Vext.

In example a), the current has to be constant, so the difference between applied voltage and generated voltage has to be constant, too. 50 % of voltage results in a bit less than 50 % of speed but the current is still 100 %, resulting in about 50 % power.

In example b), speed, force, and current decrease, so with 50 % voltage you might get about 50 % speed, and 25 % current, resulting in 12.5 % power.

I don't think the Joerg Fricke's answer is right as to the b) example. when driving a fast vehicle on a horizontal plane , then 50% of voltage not must results in 50% of speed . Generally the speed is a bit more than 50% of the original speed .

If you are interested only in procedure to calculate the average current and voltage, mathematically the procedure is the same: knowing the function (waveform) in the load, the average is found integrating the function tacking in account the minimum and maximum values of the function (Imin and Imax or Vmin and Vmax) and dividing by the period. But take in mind that the waveform of the current over the load will be a increasing/decreasing exponential and the voltage will be square wave. The average current or voltage of course will be dependent of the duty cycle. To the voltage, a duty cycle of 50% (considering square wave without distortion) means 50% of the voltage, but it is not true to the current. Here the time constant L/R affects the average current.

John Sinoy

You are right: With the assumptions mentioned above (except Vext - Vgen 0, in the second case, impedance -> infinity. Both cases do not correspond to real motors, but according to Vext - Vgen