A two pole, $1000hp,6000V,60Hz,$ three phase, wye$-$connected synchronous motor has an effective armature resistance of $0\mathrm{.}52$ and a synchrounous reactance of $4,2$ per phase. The efficiency of the motor at the rated load, $0,8PF$ leading is $92\%$ neglecting field losses due to dc excitation, calculate

a$)$ The generated emf per phase

b$)$ The torque angle

c$)$ The mechanical power developed by the armature at the rated load

d$)$ The internal torque developed.

$(20$ marks$)$