For my solution l used the rated power output to calculate the equivalent RL circuit, but that was wrong according to the solution. The solution used the rated power input. I would like to know why ?

 

For my solution l used the rated power output to calculate the equivalent RL circuit, but that was wrong according to the solution. The solution used the rated power input. I would like to know why ?

Think of it as if you were the source providing power to this motor, which inside a black box. The source doesn't know anything about the motor inside the black box. It doesn't know what it's output power is, nor does it know the efficiency at which the motor is operating. The only thing the source knows is what input power the motor is demanding.

So if we wanted to model the motor hidden inside the black box, it only makes sense to use the input power of the motor.