A $3-$phase, star connected, $440$ V$,60$ Hz$,8-$pole squirrel$-$cage induction motor has the following

parameters $($ohms$/$phase$)$ referred to the stator:

$//$ R $0\mathrm{.}085,$ R $0\mathrm{.}067,$ X $0\mathrm{.}196,$ X $0\mathrm{.}161,$ X $6\mathrm{.}65,$ R $45\mathrm{.}51212$ m c $======$

a$)$ Determine the starting torque and the supply starting current if the motor is started

directly online.

b$)$ The developed torque at slip of $0\mathrm{.}05.$

c$)$ The pull$-$out torque and the corresponding speed.

d$)$ Determine the staring torque and the supply starting current using:

i$.$ An auto transformer started with a $70\%$ tapping.

ii$.$ A star$-$delta starter.