The transformer of Problem 3.16 is supplying a rated load of \(50 \mathrm{kVA}\) at a rated sec ondary voltage of \(240 \mathrm{~V}\) and at 0.8 power factor lagging. Neglect the transformer exciting current.

(a) Determine the input terminal voltage of the transformer on the high-voltage side.

(b) Sketch the corresponding phasor diagram.

(c) If the transformer is used as a step-down transformer at the load end of a feeder whose impedance is \(0.5+j 2.0 \Omega\), find the voltage \(V_{S}\) and the power factor at the sending end of the feeder.

Problem 3.16

A single-phase, \(50-\mathrm{kVA}, 2400 / 240-\mathrm{V}, 60-\mathrm{Hz}\) distribution transformer has the following parameters:

Resistance of the \(2400-\mathrm{V}\) winding: \(\mathrm{R}_{1}=0.75 \Omega\)

Resistance of the \(240-\mathrm{V}\) winding: \(\mathrm{R}_{2}=0.0075 \Omega\)

Leakage reactance of the \(2400-\mathrm{V}\) winding: \(\mathrm{X}_{1}=1.0 \Omega\)

Leakage reactance of the \(240-\mathrm{V}\) winding: \(\mathrm{X}_{2}=0.01 \Omega\)

Exciting admittance on the \(240-\mathrm{V}\) side \(=0.003-j 0.02 \mathrm{~S}\)

(a) Draw the equivalent circuit referred to the high-voltage side of the transformer.

(b) Draw the equivalent circuit referred to the low-voltage side of the transformer. Show the numerical values of impedances on the equivalent circuits.