Problem$-1(40$ Points$)$

Three parallel single$-$phase loads are supplied from a $\backslash (220-\backslash$mathrm$\{$V$\}\backslash$mathrm$\{$rms$\},60\backslash$mathrm$\{$~Hz$\}\backslash )$ single$-$phase supply. The load data is given below

Load $1$: $\backslash (30\backslash$angle $36\mathrm{.}87^\{\backslash$circ$\}\backslash )$ kVA

Load $2$: $\backslash (16\backslash$mathrm$\{$~kW$\},0\mathrm{.}85\backslash$mathrm$\{$pf$\}\backslash )$ 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?