A $3-$phase, $50$ Hz$,$ Y connected, $8$ pole synchronous generator has $2$ coil sides per slot and $12$ turns per coil. The stator of the synchronous generator has $360$ slots on its periphery. The coils used are short$-$pitched by $2$ slots. The flux per pole is $0\mathrm{.}05$ Wb$/$Pole which is sinusoidally distributed. Determine a$)$ The speed $($in RPM$)$ of the prime mover attached to the synchronous generator to maintain the $50$ Hz frequency of the generated emf. b$)$ The coil span $($in Electrical degree$)$ of the short$-$pitched coils. c$)$ The distribution factor and the pitch factor. d$)$ The line$-$to$-$line induced emf $($in kV$)$ in the synchronous generator. The alternator has a stator resistance of $0\mathrm{.}25$ per phase and the synchronous reactance of $3\mathrm{.}2$ per phase. For a lagging load current of $100$ A at $0\mathrm{.}8$ power factor, determine e$)$ The magnitude of line$-$to$-$line terminal voltage $($in kV$).$ f$)$ The load angle $($in Electrical Degree$).$ g$)$ The net reactive power $($in kVAR$)$ generated by the synchronous generator.