Electrical Power Systems Technology

Power System Fundamentals 43

Use of Vectors for Parallel AC Circuits

ector V representation is also useful for parallel AC circuit analy-

sis. Voltage in a parallel AC circuit remains the same across all the com-

ponents, and the currents through the components of the circuit can be

shown using vectors. A parallel RLC circuit is shown in Figure 2-17.

The current through the capacitor (IC) is shown leading the current

through the resistor (IR) by 90°. The current through the inductor (IL) is

shown lagging IR by 90°. Since IL and IC are 180° out of phase, they are

subtracted to find the total reactive current (IX). By drawing lines paral-

lel to IR and IX, we can find the total current of the circuit (IT). These vec-

tors form a right triangle; therefore, total current can be expressed as:

IT= IR^2 + IX^2

Figure 2-15. Voltage vector relationship in a series RLC circuit: (A) Circuit dia-

gram; (B) vector diagram; (C) problem solution