A $460-V,4-$pole,$50-hp,60-Hz,$ Y$-$connected, $3-$phase induction motor develops its fullload induced torque at $3\mathrm{.}8$ percent slip when operating at $60$ Hz and $460$ V $.$ The per phase impedances of the motor are: $R_l=0\mathrm{.}33,x_m=30,x_l=0\mathrm{.}42,x_2^{\text{'}}=0\mathrm{.}42$ Mechanical, core, and stray losses may be neglected in this problem.

a$)$ Find the value of the rotor resistance $R_2^{\text{'}}.$

b$)$ Find Tmax, smax, and the rotor speed at maximum torque for this motor.

c$)$ Find the starting torque of this motor.

$[$Ans: $($a$)0\mathrm{.}171,0\mathrm{.}0068,($b$)448N-m,0\mathrm{.}191,($c$)198N-m$