$.$ A $30$kVA $10$kV$/0\mathrm{.}525$kV$,50$Hz$,$ star$-$star $($Y$-$Y$)$ connected three phase transformer has the following parameters for each phase: R$1=43\mathrm{.}2,$ X$1$ $=46\mathrm{.}9,$ R$2=0\mathrm{.}12,$ X$2$ $=0\mathrm{.}125.$ Each phase is loaded by a load impedance of $8\mathrm{.}84$ with the power factor of $0\mathrm{.}8.$ a$.$ By using the simplest equivalent circuit, calculate the primary and secondary currents, the input power factor, the induced voltage. Find the apparent, the active and the reactive powers both for the primary and the secondary$.$ b$.$ If the primary side no$-$load current $($I$10)$ and core loss current $($I$1$FE$)$ are $80$mA and $11\mathrm{.}5$mA$,$ respectively, by using the L$-$equivalent circuit recalculate all the parameters in part $($a$).$