Problem $3(25$ points$)$

A $230V,60Hz,6-$pole, Y$-$connected three$-$phase induction motor has the following parameters in ohms$/$phase as referred to the stator:

$R_1=11\mathrm{.}8,R_2=26\mathrm{.}8,x_1=17\mathrm{.}3,x_2=13\mathrm{.}6,R_C=4500,$ and $x_m=1900$

If the rated motor speed is $1130$ rpm $,$ determine:

$($a$)$ Power input

$($b$)$ Power developed, $P_d$