A $20-$kVA $8000/480-$V distribution transformer has the following resistances and reac$-$

tances: RP $=32$

$,$ RS $=0$:$05$

$,$ XP $=45$

$,$ XS $=0$:$06$

$,$ XC $=250$k

$,$ XM $=30$k

The

excitation branch impedances are referred to as the high$-$voltage side of the transformer.

$($a$)$ Find the equivalent circuit of this transformer referred to the high$-$voltage side.

$($b$)$ Assume that this transformer supplies a rated load $(20$kVA$)$ at $480$V and $0\mathrm{.}8$PF lag$-$

ging. What is this transformer's input voltage? What is the voltage regulation?

$($c$)$ What is the transformer's eciency under part $($b$)$ conditions?