Q$2.$ A single$-$phase step$-$down transformer is rated $10$MVA,$138kV-7200V.$ The results of open$-$circuit and short$-$circuit tests are as follows:

$30$ Points

$V_{oc}=7200V,I_{oc}=20\mathrm{.}8A,P_{oc}=75kW$

$V_{sc}=9660V,I_{sc}=72\mathrm{.}46A,P_{sc}=86\mathrm{.}84kW$

$($a$)$ Calculate the rated current on each side of the transformer.

$($b$)$ Calculate the equivalent resistance $(R_{eq.p})$ and equivalent reactance $(x_{eq.p})$ referred to the transformer primary side $($Note: Use short$-$circuit test parameters$).$

$($c$)$ Calculate the equivalent core resistance $(R_{fe,p})$ and magnetizing reactance $(x_{m,p})$ referred to the transformer high side $($Note: Use open$-$circuit test parameters$).$

$($d$)$ Calculate the transformer efficiency when operating at rated voltage and rated load @unity $F_p.$