Q$3.$ A $480-$V $200-$kVA $0\mathrm{.}8-$power$-$factor$-$lagging $60-Hz$ two$-$pole Y$-$connected synchronous generator has a synchronous reactance of $0\mathrm{.}25$ and an armature resistance of $0\mathrm{.}03.$ At $60$ Hz $,$ its friction and windage losses are $6$ kW $,$ and its core losses are $4$ kW $.$ The field circuit has a dc voltage of $200$ V $,$ and the maximum $I_F$ is $10$ A $.$ The resistance of the field circuit is adjustable over the range from $20$ to $200.$ The Open Circuit Characteristics $($OCC$)$ of this generator is shown in Figure $3,$ OCC $3.$

$(40$ Points$)$

$($a$)$ How much field current is required to make $V_T$ equal to $480$ V when the generator is running at no load?

$($b$)$ What is the internal generated voltage of this machine at rated conditions?

$($c$)$ How much field current is required to make $V_T$ equal to $480$ V when the generator is running at rated conditions?

$($d$)$ How much power must the generator's prime mover be capable of supplying?

Figure: $3,$ OCC $3$