A $3-$phase induction motor has $4$ poles, it is connected in Y and rated $60$Hz $480$V $($l $$ l$).$ It has

RR $=0\mathrm{.}5$ Rs $=0\mathrm{.}2$ Lm $=250$mH Lls $=$ Llr $=5\mathrm{.}7$mH

$($a$)$ Calculate starting torque and current under rated conditions of voltage and frequency. Calculate

input power.

$($b$)$ What is the speed and torque for rated conditions at maximum torque?

$($c$)$ If the frequency and voltage are lowered to maximize torque at starting, calculate this torque,

frequency and corresponding current, power factor and input power