List three functions which a transformer may perform in an electrical circuit. $[3$ marks$]$Tests are performed on a single phase, $10$ kVA, $2200/220$ V$,60$ Hz transformer and the following results are obtained:Open$-$Circuit Test $($Measured in the Secondary$)$ Short$-$Circuit Test$($Measured in the Primary$)$

Voltmeter Ammeter Wattmeter $220$ V $2\mathrm{.}5$ A $100$ W $155$ V$4\mathrm{.}6$ A$220$ W

$($a$)$ Derive the parameters for the approximate equivalent circuit of the transformer

referred to the low$-$voltage side and the high$-$voltage side; $($b$)$ Express the excitation current as a percentage of the rated current; $($c$)$ Determine the power factor for the no$-$load and short$-$circuit tests; $[7$ marks$][2$ marks$][2$ marks$]($d$)$ Determine the voltage regulation in percent for $75\%$ full load and $0\mathrm{.}6$ power factorleading. Neglect core losses$[6$ marks$]$