A $100-$MVA $12\mathrm{.}5-$kV $0\mathrm{.}85-$PF$-$lagging $50-$Hz two$-$pole Y$-$connected synchronous generator has a

per$-$unit synchronous reactance of $1\mathrm{.}1$ and a per$-$unit armature resistance of $0\mathrm{.}012.$

$($a$)$ What are its synchronous reactance and armature resistance in ohms?

$($b$)$ What is the magnitude of the internal generated voltage EA at the rated conditions? What is its

torque angle at these conditions?

$($c$)$ Ignoring losses in this generator, what torque must be applied to its shaft by the prime mover

at full load?