A single phase, $100$ kW$,220/110$V transformer, has the following parameters:

R$1=0\mathrm{.}02,$ R$2=0\mathrm{.}008,$ X$1=0\mathrm{.}03,$ X$2=0\mathrm{.}0075,$ Rc$=250,$ Xm$=125$

The transformer is supplying $50\%$ of its full load at unity power factor and nominal secondary

voltage.

a$)$ Draw the approximate equivalent circuit of this transformer, showing the values of the

elements referred to the primary side.

b$)$ Determine the input voltage and current of the transformer $($in polar form$).$

c$)$ Calculate the transformer voltage regulation and efficiency