Problem $2[30$ points$]$:

Consider the electric circuit shown below:

Assume: $Z_{Ln}=0\mathrm{.}4+j0\mathrm{.}4=\frac{0\mathrm{.}283}{{?}_{45}},C=0\mathrm{.}5mF,=377$ Assume the complex power consumed by the load is: $S_{Ld}=3600W+j3600$VAR

$($a$)-$ Find the power factor of the load $(p{f}_{Ld})$ and determine it is lead or lag.

$($b$)-$ Find the reactive power generated by the capacitor $(Q_C).$

$($c$)-$ For the combined load and the capacitor, find the total consumed complex power $(S_{Ld+C})$ and the related power factor $(p{f}_{Ld+C}).$

$($d$)-$ Find the line current $(I_{Ln}).$

$($e$)-$ Find the active power lost in the line $(P_{Ln}).$

Solution: