A $230$ V$,4-$pole, $50$ Hz single$-$phase induction motor has following equivalent circuit

parameters:

R$1=2\mathrm{.}8,$ X$1=3\mathrm{.}8,$ Xm$=82,$ R$2=4\mathrm{.}8,$ X$2=3\mathrm{.}6$

The core losses are $32$ W and friction & windage losses are $18$ W$.$ At the full load slip of $0\mathrm{.}04,$ find $($a$)$ total impedance of the motor $($b$)$ the input current of the motor $($c$)$ the power factor at the input $($d$)$ net mechanical power output $($e$)$ speed at full load $($f$)$ net output torque $($g$)$ efficiency.