$2.$ The single$-$phase equivalent parameters for a $3-,$ Wye$-$connected, four pole induction motor in $/$phase are

R$1=0\mathrm{.}17$ X$1=1\mathrm{.}05$ R$2=0\mathrm{.}24$ X$2=0\mathrm{.}87$ Rc $=435$ Xm $=82\mathrm{.}1$

For all problems, assume a terminal voltage of $460$ VLL 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 $($Rc$),$ if the rotor is locked at zero speed, find the torque

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