Task $3$

$(25$ pts$)$

A $2200/110-$V transformer rated at $\backslash (50-\backslash$mathrm$\{$kVA$\},\backslash$mathbf$\{50$ H z$\}\backslash )$ has been through an opencircuit test and short$-$circuit test, of which the results are shown in the following table.

$($a$)$ Find the equivalent circuit of this transformer referred to the high$-$voltage side of the transformer.

$($b$)$ Assume that this transformer is supplying rated load at $110$ V $.$ Calculate the transformer's input voltage when the loading at the secondary is $0\mathrm{.}8$ pf lagging, unity pf and $0\mathrm{.}8$ pf leading.

$($c$)$ Determine the percentage voltage regulation and efficiency at full load and $0\mathrm{.}8$ pf lagging.

$($Note: pf stands for power factor.$)$