$3)$ A $3-$ph $400V,30$KVA,$50hz,10$ pole $Y$ synchronous generator has synchronous reactance of $j4\mathrm{.}5$ ohms and armature resistance as $0\mathrm{.}2$ ohms $.$

If the generator is supplying the rated current at $0\mathrm{.}93$ p$.$f$.$ leading

$($a$)$ Find the Internal generated voltage and the torque angle of the generator.

$($b$)$ If the core loss of the generator is $1000$ W and the mechanical losses are $1500$ W $,$ find the input power and the torque required for the above conditions

$($c$)$ Find the efficiency in the above conditions.