$2.)$ A $15$ kVA single$-$phase transformer of $\frac{4160}{240}V$ has core losses of $120$ W $.$ The resistance in values per unit is $0\mathrm{.}01$ and the reactance per unit equals $0\mathrm{.}06.[20$pt$]$

a$)$ What is the equivalent impedance of the transformer referred to on the $4160$ V side?

b$)$ What voltage must be applied to the $4160$ winding to obtain $240$ V at the low voltage side terminals when the load on the low voltage side is $12$ kVA with a power factor of $0\mathrm{.}8$ lagging?

c$)$ What is the efficiency under the conditions of part $($b$)?$

d$)$ Using the unit quantities, determine the regulation at full load when the power factor is $0\mathrm{.}8$ leading and $0\mathrm{.}8$ lagging.