$4-15.$ A three$-$phase, Y$-$connected synchronous generator is rated $120$ MVA, $13\mathrm{.}8$ kY$,0\mathrm{.}8$ PF$-$Iagging, and $60$ Hz$.$ Its synchronous reactance is $1\mathrm{.}2$ n$.$ per phase, and its arma ture resistance is $0\mathrm{.}1$ n$.$ per phase. $($a$)$ What is its voltage regulation? $($b$)$ What would the voltage and apparent power rating of this generator be if it were operated at $50$ Hz with the same armature and field losses as it had at $60$ Hz$?($c$)$ What would the voltage regulation of the generator be at $50$ Hz$?$