The synchronous reactance of a $2200-$V$,$ three$-$phase, Y$-$connected, synchronous motor is $8$ W$/$phase$,$ and the armature$-$winding resistance is negligible. At full load, the motor takes $90$ kW at $0\mathrm{.}8$ pf leading. If the load torque is held constant, but the field excitation is increased by $30\%,$ determine $($a$)$ the new torque angle, $($b$)$ the armature current, and $($c$)$ the power factor.