Problem $5$: A $3-$phase induction motor is connected to a voltage source with $v_s(t)=140cos(400t)V_{rms}.$ The motor has $R_s=4,R_r^{\text{'}}=0\mathrm{.}5,x_s=2,x_r^{\text{'}}=10,$ and $x_m=50.$

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, $T_{\text{d}\text{e}\text{v}},$ 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, $T_{\text{d}\text{e}\text{v}\text{,}}$ is $6$ Nm $?(10$ points$)$