A $4000$ V$,50$ Hz$,150$ kVA, $4$ pole star connected synchronous

generator has an effective armature resistance is $0\mathrm{.}3.$ The

generator produces a short circuit current of $200$ A$,$ and open circuit voltage is $1000$ V$($line$).$ Calculate

$($i$)$ The rotational speed $($ii$)$ Synchronous impedance per phase $($iii$)$ Synchronous reactance per phase $($iv$)$ Armature current

$($v$)$ Generated emf and at $0\mathrm{.}8$ power factor lagging