The single$-$phase equivalent parameters for a $3-,$ Wye$-$connected, four pole induction motor in $\frac{}{?}$ phase are

$R_1=0\mathrm{.}17x_1=1\mathrm{.}05$

$R_2=0\mathrm{.}24x_2=0\mathrm{.}87$

$R_c=435x_m=82\mathrm{.}1$

For all problems, assume a terminal voltage of $460V_{LL}$ and electrical frequency of $60$ Hz $.$ The Mot power rating is

$($a$)$ For a slip of $3\mathrm{.}2\%,$ calculate the motor phase current and both, the real and reactive input power

$($b$)$ For a slip of $3\mathrm{.}2\%,$ calculate mechanical speed in revolutions per minute $($ rpm $),$ calculate mechanical output power, and the power dissipated in the rotor if the friction and windage losses of the motor are $270$ W

$($c$)$ For a slip of $3\mathrm{.}2\%,$ calculate, the stator winding losses, rotor winding losses, mechanical losses $($using friction and windage losses from the previous problem$)$ and core loss of the motor. Also, find the motor efficiency from electrical stator input to mechanical shaft output.

$($d$)$ Neglecting the core loss $(R_c),$ if the rotor is locked at zero speed, find the torque

$($e$)$ Neglecting the core loss $(R_c),$ find that maximum torque produced by the motor $($pull$-$out torque$)$ and the slip and rotor speed at which that torque occurs.