A three phase, $120V,60Hz,Y-$ connected sixpole synchronous generator has the OCC shown $(V_{T}vS{I}_F).$ This generator has a synchronous reactance of $j0\mathrm{.}5$ and an armature resistance of RA $0\mathrm{.}02.$

$1.S$ a$)[2$ pts$]$ How much field current is required to make $V_T$ equal to $120$ V when the generator supplies $200$ A at $0\mathrm{.}8$ PF lagging.

$1\mathrm{.}5$ b$)[2$ pts$]$ Find the input power if the core loss is $1$ kW $,$ friction & windage loss is $1\mathrm{.}5$ kW $.$

c$)[2$ pts$]$ How much torque must the generator's prime mover be capable of supplying?