Problem $1.$ A $80$ MVA, $14\mathrm{.}4$ kV$,0\mathrm{.}85$ lagging, four pole, three phase, Wye connected, $60$ Hz synchronous generator has a synchronous reactance of Xs $=2\mathrm{.}3$ and armature resistance of Ra $=0\mathrm{.}03.($a$.)$ What is the internal generated voltage at rated conditions? What is the power angle? $($b$.)$ If the friction and windage losses at $400$ kW and the core loss is $500$ kW$,$ what is the motor$$s efficiency? $($c$.)$ What applied torque is needed at full load$/$rated load?