A $3-$phase, $460-V,60-Hz,4-$pole $Y$ connected induction motor has the following parameters:

$R_1=1\mathrm{.}01$;$R_2^{\text{'}}=0\mathrm{.}69$;$,x_1=1\mathrm{.}3$;$x_2^{}=1\mathrm{.}94$;$,x_m=43\mathrm{.}5$;

The no$-$load loss, $P_{no\text{l}\text{o}\text{a}\text{d}},$ is negligible. The load torque, which is proportional to the speed squared, is $41$ Nm at $1740$ rpm $.$ The motor speed is $1550$ rpm $.$

$($a$)$ Draw the approximate circuit.

$($b$)$ Determine the load torque $T_L.$

$($c$)$ Determine the motor input current, $I_1.$

$($d$)$ Determine the motor rotor current $I_2^{}.$

$($e$)$ Determine the magnetizing current, $I_{}.$

$($f$)$ Determine the motor input power $P_i.$

$($g$)$ Determine the slip for maximum current, $s_{\text{T}\text{m}\text{a}\text{x}}.$

$($h$)$ Determine maximum rotor current $I_{2(max)}^{}.$

$($i$)$ Determine the speed at maximum rotor current ${}_{\text{m}\text{a}\text{x}}-$

$($j$)$ Determine the torque at the maximum current $T_m$

PLEASE ANSWER ALL PARTS