A $3-$phase, $4-$pole, Y$-$connected synchronous generator is rated $1\mathrm{.}5$MVA,$22kV($line$,$ rms$),50$ Hz and has a non$-$salient type rotor. The machine has a per$-$phase synchronous reactance of $25,$ armature resistance of $1,$ and is connected to an infinite bus with a line voltage of $22$ kV $($rms$).$ The generator runs at synchronous speed. The effects of magnetic saturation can be neglected.

$($a$)$ When the field excitation current is adjusted to $72$ A $,$ the generator supplies its rated current at a power factor of $0\mathrm{.}9($lagging$).$

Determine:

$($i$)$ The armature phase voltage generated.

$($ii$)$ The armature to field mutual inductance.

$($b$)$ Sketch the phasor diagram for Part $($a$),$ showing all currents and voltage phasors.