A $100-$kVA, $8000/277-$V distribution transformer has the following resistances and reactances: RP $=5,$ RS $=0\mathrm{.}005,$ XP $=6,$ XS $=0\mathrm{.}006,$ RC $=50$k$,$ XM $=10$k$.$ The excitation branch impedances are given referred to the high$-$voltage side of the transformer. a$)$ Find the equivalent circuit of this transformer referred to the low$-$voltage side. b$)$ Find the per$-$unit equivalent circuit of this transformer. c$)$ Assume that this transformer is supplying rated load at $277$ V and $0\mathrm{.}85$ PF lagging. What is this transformer$$s input voltage? What is its voltage regulation? d$)$ What are the copper losses and core losses in this transformer under the conditions of part $($c$)?$ e$)$ What is the transformer$$s efficiency under the conditions of part $($c$)?$