Question $4[15$ points$]$:

Consider a $120-$kVA,$\frac{4800}{240}V$ single$-$phase power transformer driving a load of lagging power factor of $0\mathrm{.}85.$ Its equivalent primary series resistance $R_{\text{e}\text{q}\text{P}}$ is $1\mathrm{.}96$ and the core loss resistance $R_C$ is measured to be $60k.$ Calculate the following referred to the primary side of the transformer:

$($a$)$ rated full$-$load current $I_P=\frac{s}{V_P},$

$($b$)$ output load real power $P_{\text{o}\text{u}\text{t}}=$Scos$,$

$($c$)$ Cu or winding loss $P_{Cu},$

$($d$)$ core loss $P_{\text{c}\text{o}\text{r}\text{e}}=\frac{(V_P{)}^2}{R_C},$

$($e$)$ input power $P_{in}=P_{\text{o}\text{u}\text{t}}+P_{Cu}+P_{\text{c}\text{o}\text{r}\text{e}},$ and

$($f$)$ efficiency $=\frac{P_{\text{o}\text{u}\text{t}}}{P_{in}}100\%$