As shown in Fig. 54, given two impedances connected in parallel, they can be replaced by a resistor and a reactive element connected either in series or in parallel.
Equation (327) shows how we get the equivalent circuits.
Given a load consisting of a resistor and an inductor, the power factor due to the load is lagging and it may be low. It can be be improved by connecting a capacitor, as shown Fig. 55.
The relevant equations are presented now. The load current can be found, as expressed by equation (328). Given the desired power factor, the power factor angle can be found out. Since the source current has a phase of fo, the real and the imaginary parts of source current are related as shown by equation (329). The real part of source current is the same as the real part of the load current, and hence the imaginary part of the source current can be found out, as shown by equation (330). The capacitor current can be determined, as shown by equation (331). Equation (332) shows how the required capacitive reactance can be determined.