A three$-$phase $138$ kV$/12\mathrm{.}47$ kV Y distribution substation transformer rated $45$ MVA OA$/60$ MVA FA$/75$MVA FOA has an $8\%$ impedance. $($a$)$ Determine the rated current on the primary distribution side of the transformer at its OA$,$ FA$,$ and FOA ratings. $($b$)$ Determine the per$-$unit transformer impedance using a system base of $100$ MVA and $12\mathrm{.}47$ kV on the primary distribution side of the transformer. $($c$)$ Calculate the short$-$circuit current on the primary distribution side of the transformer for a three$-$phase bolted fault on the primary distribution side. Assume that the prefault voltage is $12\mathrm{.}47$ kV