Chapter 2, Problem 2.21P

An industrial plant consisting primarily of induction motor loads absorbs 500 kW at 0.6 power factor lagging. (a) Compute the required kVA rating of a shunt capacitor to improve the power factor to 0.9 lagging. (b) Calculate the resulting power factor if a synchronous motor rated at 500 hp with $90\%$ efficiency operating at rated load and at unity power factor is added to the plant instead of the capacitor. Assume constant voltage $(\text{1 hp}=0.\text{746 kW})$.