A single phase,$25$kVA,$220440$V$,60$Hz $$transformer gave the following test results.

Open circuit test $(440$V $$side open$)$: $220$V$,9\mathrm{.}5$A$,650$W

Short$-$circuit test $(220$V side shorted$)$: $37\mathrm{.}5$V$,55$A$,950$W

$($a$)$Derive the approximate equivalent circuit in per$-$unit values.

$($b$)$Determine the voltage regulation at full load, $0\mathrm{.}8$PF $$lagging$.$