Q$4(10$ points$)$

The three loads in Fig below are fed from a line having a series impedance $0\mathrm{.}01+$j$0\mathrm{.}08$ Omega.

Load $1$ absorbs $16$ kW and $18$ kVAR;

Load $2$ absorbs $10$ kVA at $0\mathrm{.}6$ leading; and

Load $3$ absorbs $8$ kW at unity power factor

$($a$)$ Find the impedance that is equivalent to the three parallel loads. Find the power factor of this equivalent impedance, is it

leading or lagging?

$($b$)$ Calculate the rms value of the voltage $($Vs$)$ at the sending end of the line.

$($c$)$ Calculate the average and reactive powers associated with the line impedance.

$($d$)$ Calculate the average and reactive powers associated with the source $($Vs$)).$