A $\backslash (61\mathrm{.}2\backslash$mathrm$\{$kV$\}\backslash$cdot $\backslash$mathrm$\{$A$\}\backslash )$ step$-$up transformer with a winding ratio of $\backslash (400$: $600\backslash )$ is fed from a wall outlet $\backslash ((120\backslash$mathrm$\{$~V$\},60\backslash$mathrm$\{$~Hz$\})\backslash ).$ It is found that when a certain load is attached the secondary current drawn is $68$A$,$ the power factor is $0\mathrm{.}92$ lagging, and the efficiency is $\backslash (94\mathrm{.}6\backslash \%\backslash ).$

$($a$)$ Determine the output voltage applied to the load.

$($b$)$ How much $($real$)$ Power is being delivered to the load?

$($c$)$ Find the current in the primary coil.

$($d$)$ Determine the total power loss in the transformer.

$($e$)$ What fraction of a full$-$load is operating from this transformer?