Electrical Power Systems Technology

46 Electrical Power Systems Technology

Z = R^2 + XL– XC

2

100

(^2) + 376.8 – 265.4 2

10,000Ω 12,410+ Ω

Z = 149.7 Ω

This formula may be clarified by using the vector diagram shown
in Figure 2-17. The total reactance (XT) of an AC circuit may be found
by subtracting the smallest reactance (XL or XC) from the largest reac-
tance. The impedance of a series AC circuit is determined by using the
preceding formula, since a right triangle (called an impedance triangle) s i
formed by the three quantities that oppose the flow of alternating cur-
rent. A sample problem for finding the total impedance of a series AC
circuit is shown in Figure 2-17.

Impedance in Parallel AC Circuits
When components are connected in parallel, the calculation of im-
pedance becomes more complex. Figure 2-18 shows a simple parallel
RLC circuit. Since the total impedance in the circuit is smaller than the
resistance or reactance, an impedance triangle, such as the one shown
in the series circuit of Figure 2-17, cannot be developed. A simple meth-
od used to find impedance in parallel circuits is the admittance triangle,
shown in Figure 2-18B. The following quantities may be plotted on the
triangle:

1 1 1
admittance = — , conductance = — , inductive susceptance = —
Z R XL

1
and capacitive susceptance = —
XC

Notice that these quantities are the reciprocals of each type of op-
position to alternating current. Therefore, since total impedance (Z) is the
smallest quantity in a parallel AC circuit, it becomes the largest value on
the admittance triangle. The sample problem of Figure 2-18 shows the
procedure used to find total impedance of a parallel RC circuit.