$($a$)$ Two generators rated $100$ MW and $200$ MW are operating in parallel. The droop characteristics of their governor are $\backslash (4\backslash \%\backslash )$ and $\backslash (3\backslash \%\backslash )$ respectively from no$-$load to fullload. Assuming that the generators are operating at $50$ Hz on no$-$load, how would a load of $50$ MW be shared between them? What will be the system frequency at this load?

$($b$)$ A three$-$phase, Y$-$connected induction load is supplied by a three$-$phase and four$-$wire system with line$-$line voltage of $220$ V $($rms$)$ and the impedances of the load is $\backslash ((5+$j $4)\backslash$Omega $\backslash )$ per phase. Determine the magnitude of the line current and the power factor of the load.

$($c$)$ The blade length of a wind turbine is $8$ m and power coefficient Cp is $0\mathrm{.}35.$ Compute the power captured by the blades when wind speed is $\backslash (4\mathrm{.}0\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ in a site where air density is $\backslash (1\mathrm{.}5\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$m$\}3\backslash ).$