$7\mathrm{.}8$ A $3-$phase, $5$kW$,440$V$,50$Hz$,4$ pole, Y$-$connected field current of $1$ A $.$ When operating at full load the

of $0\mathrm{.}2$ Omega, synchronous reactance of $8$Omega and for load

power factor is unity.

$($i$)$ Calculate the torque angle when operating at full load

$($ii$)$ Pull$-$out torque

$($iii$)$ Power factor, armature current and efficiency at half the rated torque.