A three phase, $440$ V $($line to line$),60$Hz$,$ Y$-$ connected, $8$ poles $100$ hp inductionmotor has the following equivalent circuit parameters expressed in Ohms per phase referred tothe stator:R$1=0\mathrm{.}06,$ R$2=0\mathrm{.}05,$ X$1=$ X$2=0\mathrm{.}26,$ Xm $=8\mathrm{.}8$The combined rotational and core losses are $3600$ Watts at rated shaft output, and can betaken 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 VT H $,$ RT H $,$ jXT H $,$ R$2,$ X$2$ for a slip, s$,$ amd drawa 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