A $10-$hp$,208-$V$,60-$Hz$,6-$pole, three$-$phase, Y$-$connected, synchronous motor has a synchronous impedance of $0\mathrm{.}25+$ j$3\mathrm{.}5$ W$/$phase$.$ The friction and windage loss are $450$ W$,$ the core loss is $250$ W$,$ and the field$-$excitation loss is $100$ W$.$ Determine $($a$)$ the armature current, $($b$)$ the torque angle, $($c$)$ the shaft torque, and $($d$)$ the efficiency when the motor operates at full load with a unity power factor.