Problem 107-5    Source:  Problem prepared by the website author.

A 380 V three-phase induction motor, 6 poles, 60 Hz and 50 HP, develops full power with 4% slip. The mechanical losses are 900 W. Find the following quantities:

a) The power in the air gap, P_gap ;

b) The torque (torque) on the motor shaft, τ_ind ;

c) Rotor copper losses, P_jr;

Solution of the Problem 107-5   

Item a

Let's calculate the rated power, P_n, in watts.

Using the eq. 107-31 it is possible to calculate the mechanical power of the rotor, or:

And since we know about slip, we can easily calculate the power in the air gap using eq. 107-30.

Item b

To calculate the torque of the machine, we will first calculate the synchronous speed, using eq. 107-02.

Let's transform n_sync to ω_sync

Therefore, the torque developed by the machine is given by eq. 107-32, or:

Doing the math, we find:

Item c

Using the eq. 107-27 we can calculate the rotor copper losses, or: