$.$ A $5$ kW$,3-$phase, $440$ V$,50$ Hz$,4-$pole, unity power factor, delta connected permanent magnet synchronous motor has XS $=12$ and negligible RS$.$ Motor is controlled by variable frequency control with a constant V$/$f ratio up to base speed and constant terminal voltage above the base speed. Calculate i$.$ Armature current and power factor for $40\%$ of rated motor torque and $2000$ rpm$.$ ii$.$ Motor torque for $2000$ rpm and $0\mathrm{.}5($leading$)$ power factor operation. iii. Armature current and power factor for regenerative braking power output of $2$ kW at $2000$ rpm$.$ iv$.$ Torque and power factor for regenerative braking power output of $1\mathrm{.}5$ kW$,$ rated armature current and $2000$ rpm$.$