$2.($a$)$ A $12$ kVAt $1,000/100$ V$,50$ Hz$,$ single$-$phase transformer has the following test results:

OC test $($on LV side$)$: $100$ V$,0\mathrm{.}7$ A$,85$ W

SC test $($on HV side with $100$ V side short circuited$)$: $60$ V$,12$ A$,95$ W

Determine the following:

Core loss of the transformer.

$(1$ mark$)$

$($ii$)$ Equivalent resistance and leakage reactance referred to as High Voltage $($HV$)$ side.

$(5$ marks$)$

$($iii$)$ Equivalent resistance and leakage reactance referred to as Low Voltage $($LV$)$ side.

$(2$ marks$)$

$($iv$)$ Voltage Regulation of the transformer at full load at $0\mathrm{.}8$ power factor lagging.

$(3$ marks$)$

$($v$)$ Transformer terminal voltage at full load at $0\mathrm{.}8$ power factor lagging.

$(1$ mark$)$

$($vi$)$ Efficiency of the transformer at full load $0\mathrm{.}8$ power factor lagging.

$(5$ marks$)$

$[$Cont$...$

$[$Cont$..\mathrm{.}2.$

$($b$)$ A $500$ kVA single$-$phase transformer has an efficiency of $95\%$ at full$-$load with unity power factor and also at $60\%$ of full$-$load with unity power factor. Determine the efficiency of the transformer at $75\%$ of full$-$load at $0\mathrm{.}8$ power factor.