A $100-$kVA, $2500/125-$V$,50-Hz,$ step$-$down transformer has the following parameters: $R1=1\mathrm{.}5,x1=2\mathrm{.}8,R2=15m,x2=20m,Rc1=3k,xm1=5k$

The transformer delivers $85\%$ of the rated load at a terminal voltage of $115$ V and a power factor of $0\mathrm{.}866$ lagging. Determine $($a$)$ the efficiency, and $($b$)$ the voltage regulation. Draw the phasor diagram of the transformer.

Use the approximate equivalent circuit referred to the secondary side.