The internal generated voltage, E A of a Y$-$connected, three$-$phase synchronous generator is $14\mathrm{.}4$ kV$,$ and the terminal voltage, V T $,$ is $12\mathrm{.}8$ kV$.$ The synchronous reactance of this machine is $4,$ and the armature resistance can be ignored.

$($i$)$ If the torque angle of the generator, $,$ is equal to $18,$ how much power is being supplied by this generator at the current time?

$($ii$)$ What is the power factor of the generator at this time?

$($iii$)$ Ignoring losses in this generator, what would be the value of the torque that must be applied to its shaft by the prime mover?