A $460-V,60-Hz,$ four$-$pole, Y$-$connected induction motor is rated at $25$ hp $.$ The equivalent circuit parameters are:

$R_1=0\mathrm{.}15,R_2=0\mathrm{.}154,x_M=20,x_1=0\mathrm{.}852,x_2=1\mathrm{.}066$

$P_{\text{F}\text{i}\text{c}\frac{?}{?}\text{\&}\text{W}\text{i}\text{n}}=400W,P_{\text{m}\text{i}\text{s}\text{c}}=150W,P_{\text{c}\text{o}\text{r}\text{e}}=400W$

For a slip of $0\mathrm{.}02.$ find

$($a$)$ The line current $I_L$

$($b$)$ The stator power factor

$($c$)$ The rotor power factor

$($d$)$ The rotor frequency

$($e$)$ The stator copper losses $P_{SCL}$

$($f$)$ The air$-$gap power $P_{AG}$

$($g$)$ The power converted from electrical to mechanical form $P_{\text{c}\text{o}\text{n}\text{v}}$

$($h$)$ The induced torque $T_{\text{i}\text{n}\text{d}}$

$($i$)$ The load torque $T_{\text{l}\text{o}\text{a}\text{d}}$

$($j$)$ The overall machine efficiency $$

$($k$)$ The motor speed in revolutions per minute and radians per second