A $460V,100-hp,4-$pole, $-$connected, $60-Hz,3-$phase induction motor has a full$-$load slip of $5$ percent, an efficiency of $92$ percent, and a power factor of $0\mathrm{.}87($lagging$).$ At start$-$up the motor develops $1\mathrm{.}9$ times the full$-$load torque but draws $8\mathrm{.}5$ times the rated current at the rated voltage. This motor is to be started with reduced voltage.

$($a$)$ What should be the reduced supply voltage so that the starting torque is equal to the rated torque of the motor?

$($b$)$ What will be the motor starting current at this voltage?

$[$Ans: $($a$)333$ V $,($b$)716$A$]$ji