A $100$kVA,$7200-480V,60Hz$ single$-$phase transformer has the following parameters $($in ohms$)$:

$R_{LS}=0\mathrm{.}00800,R_{HS}=1\mathrm{.}96,R_{\text{f}\text{e}\text{H}\text{S}}=53\mathrm{.}2$

$x_{LS}=0\mathrm{.}01510,x_{HS}=4\mathrm{.}55,x_{MHS}=7800$

This transformer is operated in step$-$down mode and delivers $75\%$ of its rated power to a load with a power factor of $0\mathrm{.}93$ lagging.

Tasks:

Draw the equivalent circuit model of the transformer with the equivalent series impedances referred to the high$-$voltage side.

Find the total input impedance Zin of the transformer at the high side.

Calculate the input impedance Zin with the load disconnected.

Determine the input voltage at $75\%$ load required to maintain the rated load voltage.

Calculate the exciting current when the load is disconnected.