An industrial plant consisting primarily of induction motor loads absorbs \(500 \mathrm{~kW}\) at 0.6 power factor lagging.

(a) Compute the required \(\mathrm{kVA}\) 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 \(500 \mathrm{hp}\) with \(90 \%\) efficiency operating at rated load and at unity power factor is added to the plant instead of the capacitor. Assume constant voltage ( \(1 \mathrm{hp}=0.746 \mathrm{~kW})\).