Question 

Show how the power that is transferred across the air gap of a 3phase induction motor is represented explain the trms what portion of this is useful power.

Power transferred across air gap can be represented as

Stator Iron loss (consisting of eddy and hysteresis losses) depends on the supply frequency and the flux density in the iron core. It is practically constant

The iron loss of the rotor is, however, negligible because frequency of rotor currents under normal running conditions is always small.

Total rotor cu loss = 3 [I2]2 R2

Slip is the difference between sync speed and the motor speed and normally represented in %age.

Slip % = Ns –N / Ns x 100 %

Hence it is desired to run the motor keeping the slip as small as possible.