A $3-$phase induction motor is connected to a voltage source with $140$ cos $400$s rmsv t t V$.$ The

motor has $4$sR $,0\mathrm{.}5$rR$,2$sX $,10$rX $,$ and $50$mX $.$

a$)$ If the motor is spinning at a speed of $1300$ rpm while operating in its normal operating range, how

many poles does the motor probably have? $(5$ points$)$

b$)$ What is the developed torque, Tdev $,$ for the motor when spinning at the speed from part a$?(10$ points$)$

c$)$ What are all of the possible slip values if the developed torque, T dev $,$ is $6$ Nm$?(10$ points$)$