3. The loading of a factory on a 1000 V, 50 Hz system includes: 20 kW heating (unity power factor) 10 kW (Pi) induction motors (0.7 lagging power factor) 5 kW lighting (0.85 lagging power factor) (a) Establish the power triangle for the total loading on the supply. (3 marks) (b) Determine the power-factor capacitor required to raise the power factor to unity.(4 marks) (c) Determine the change in supply current from the uncompensated to the compensated system. (3 marks)

Fig: 1