A $3-$phase induction motor has a $4-$pole star$-$connected stator winding and runs on a

$220$V$,50$Hz supply. The rotor resistance is O$.$ lQ per phase and the standstill rotor

reactance is $0\mathrm{.}90$ per phase. The ratio of stator to rotor turns is $1\mathrm{.}75.$ The full load slip

is $5\%.$ Calculate:

a$)$ The total torque, b$)$ the power output: c$)$ the maximum torque and d$)$ the speed at

maximum torque.