A three phase, $440$ V $($line to line$),60$Hz$,$ Y$-$ connected, $8$ poles $100$ hp induction motor has the following equivalent circuit parameters expressed in Ohms per phase referred to the stator: R$1=006$ R$2=005$ X$1=$X$2=026$ Xm $=88$ The combined rotational and core losses are $3600$ Watts at rated shaft output, and can be taken constant over the normal operating range. The motor is directling connected to a $440$V$,3-$phase source. $($a$)$ Derive the Thevenin equivalent circuit with VTHRTH jXTHR$2$X$2$ for a slip, s$,$ amd draw a schematic of the circuit. $($b$)$ For a slip of $2\mathrm{.}363\%,$ find out $($b$\mathrm{.}1)$ the motor speed in rpm $($b$\mathrm{.}2)$ the rotor circuit developed power and developed torque $($b$\mathrm{.}3)$ the output shaft power and output shaft torque $($b$\mathrm{.}4)$ the input power, the line current and power factor, as well as overall motor efficiency $($c$)$ Find the starting slip and torque, maximum torque and slip at maximum torque