Problem $5).[25$ PT$]$ The single phase equivalent circuit of a three$-$phase, Y $-$connected, four pole induction motor is shown in Figure. For the purposes of this problem, we will assume armature resistance is negligible. The machine is connected to a three$-$phase voltage source with lineneutral voltage of $200$ volts, RMS $(346$ volts, line$-$line$).$ The motor synchronous speed is $200$ radians$/$second and motor reaches peak torque at a speed of $160$ radians$/$second$.$

i$)[4$ PT$]$ Calculate the synchronous speed $($rpm$)$ and speed at maximum torque in rpm$.$ Also, calculate the frequency of supply voltage.

ii$)[8$ PT$]$ Calculate and draw the Thevenin equivalent of this circuit. Include the parameters values in the circuit.