Three parallel single$-$phase loads are supplied from a $220-$V rms$,60$ Hz single$-$phase supply. The load data is given below Load $1$: $3036\mathrm{.}87$ kVA Load $2$: $16$ kW$,0\mathrm{.}85$ pf lagging Load $3$: $5$ kvar, $0\mathrm{.}866$ pf leading Answer the following questions $($a$)[20$ Points$]$ Determine the total active, reactive, apparent, and complex power delivered by the source. $($b$)[10$ Points$]$ Determine the supply current and the load power factor. $($c$)[5$ Points$]$ Calculate the kvar rating of the capacitor required to improve the power factor of the load to $0\mathrm{.}95$ lagging. $($d$)[5$ Points$]$ Determine the supply current when the capacitor in part $($c$)$ is connected across the loads. $($e$)[5$ Points$]$ Compare the current magnitude in part $($b$)$ and part $($d$).$ Does the supply current increase or decrease? State valid reasons. $($f$)[5$ Points$]$ What are the advantages of improving the power factor?