$1.$ A $3-$phase round $($cylindrical$)$ rotor synchronous generator has the rated values of $1$ MVA, $\backslash (4\mathrm{.}6\backslash$mathrm$\{$kV$\},1500\backslash$mathrm$\{$~min$\}^\{-1\},50\backslash$mathrm$\{$~Hz$\}\backslash ).$ The armature $($stator$)$ winding resistance is $\backslash (2\mathrm{.}16\backslash$Omega $\backslash )$ and the armature winding reactance $($synchronous reactance$)$ is $\backslash (20\backslash$Omega $\backslash ).$

a$.$ Calculate the armature $($stator or output$)$ current, the output active and reactive powers while the generator supplies an inductive load with $0\mathrm{.}8$ power factor at its rated operation. For the same condition, sketch the phasor diagram and calculate the induced voltage $(\backslash (\backslash$mathrm$\{$E$\}\_\{\backslash$mathrm$\{$p$\}\}\backslash )$ or $\backslash (\backslash$mathrm$\{$U$\}\_\{\backslash$mathrm$\{$p$\}\}\backslash )),$ the load angle and internal phase angle $($the angle between $\backslash (\backslash$mathrm$\{$E$\}\_\{\backslash$mathrm$\{$p$\}\}\backslash )$ and $\backslash ($ I$\_\{1\}\backslash )).$

b$.$ Repeat $($a$)$ when the armature $($stator$)$ winding resistance is neglected.

c$.$ Calculate the armature $($stator or output$)$ current, the output active and reactive powers while the generator supplies a capacitive load with $0\mathrm{.}8$ power factor at its rated operation. For the same condition sketch the phasor diagram and calculate the induced voltage $\backslash (\backslash$left$(\backslash$mathrm$\{$E$\}\_\{\backslash$mathrm$\{$p$\}\}\backslash$right$)\backslash ),$ the load angle and internal phase angle $($the angle between $\backslash (\backslash$mathrm$\{$E$\}\_\{\backslash$mathrm$\{$p$\}\}\backslash )$ and $\backslash (\backslash$mathrm$\{$I$\}\_\{1\}\backslash )).$

d$.$ Repeat $($c$)$ when the armature $($stator$)$ winding resistance is neglected.

Use the photo as a basis when solving the question. Please write each option correctly and clearly.