A $500V,3$ phase, $6$ pole $,50$ Hz star$-$connected induction motor is working at full load with speed of $960$ rpm has the following equivalent circuit parameters :

$R_1=0\mathrm{.}12,x_1=0\mathrm{.}6,R_2=0\mathrm{.}06,x_2=0\mathrm{.}32$

$R_C=120,x_m=24,$ all in

Ohms.

and $x_m$ are measured from the stator side$).$

Stator to rotor turns ration is $1\mathrm{.}15.$ Mechanical losses$=550$ W$.$

Use the approximate equivalent circuit to calculate:

a$)$ The rotor current referred to stator

b$)$ The stator current and the motor power factor

c$)$ The induced electromagnetic torque

d$)$ The input and output powers

e$)$ The load torque

f$)$ Motor efficiency