$6\mathrm{.}18$ A $3$$,20$ kVA, $208$ V$,$ four$-$pole star$-$connected synchronous machine has a synchronous reactance of Xs $=1$:$5$ per phase. The resistance of the stator winding is negligible. The machine is connected to a $3$$,208$ V infinite bus. Neglect rotational losses. $($a$)$ The field current and the mechanical input power are adjusted so that the synchronous machine delivers $10$ kW at $0\mathrm{.}8$ lagging power factor. Determine the excitation voltage $$Ef$$ and the power angle $$$.($b$)$ The mechanical input power is kept constant, but the field current is adjusted to make the power factor unity. Determine the percent change in the field current with respect to its value in part $($a