A $208$V$,30$hp$,0\mathrm{.}85$PF leading, Y$-$connection, $60$Hz synchronous machines has a

synchronous reactance of $2\mathrm{.}2$ and a negligible armature resistance. Its friction and windage losses are $1\mathrm{.}2$kW$,$ and its core losses are $1\mathrm{.}0$kW$.$ Initially, the shaft is supplying a $10$hp load, and the motor$$s power factor is $0\mathrm{.}80$ leading.