A small manufacturing plant is located 2 km down a transmission line, which has a series reactance of 0:5 W=km. The line resistance is negligible.

A small manufacturing plant is located 2 km down a transmission line, which has a series reactance of 0:5 W=km. The line resistance is negligible. The line voltage at the plant is 480 0 V (rms), and the plant consumes 120 kW at 0.85 power factor lagging. Determine the voltage and power factor at the sending end of the transmission line by using (a) a complex power approach and (b) a circuit analysis approach.