A single$-$phase transformer is rated $100$kVA,$\frac{2400}{240}$ volts, $60$ Hz distribution transformer with the given parameters $($neglecting the excitation branch$)$:

R$1=0\mathrm{.}5$ Ohms $($Primary Winding Resistance$)$

R$2=j0\mathrm{.}005$ Ohms $($Secondary Winding Resistance$)$

X$1=2\mathrm{.}0$ Ohms $($Primary Leakage Reactance$)$

X$2=0\mathrm{.}02$ Ohms $($Secondary Leakage Reactance$)$

$(50$ points$)$

a$)$ Draw the equivalent circuit referred to the high voltage side

b$)$ Draw the equivalent circuit referred to the low voltage side

c$)$ If the transformer is supplying a rated load of $100$ KVA at rated secondary voltage of $240$ V and $0\mathrm{.}85$ PF lagging, determine the input terminal voltage of the transformer on the high$-$voltage side.