Impedance in an R-C-L series circuit is equal to the phasor sum of resistance, inductive reactance, and capacitive reactance (Figure 8).

Figure 8 Series R-C-L Impedance-Phasor

Equations (8-12) and (8-13) are the mathematical representations of impedance in an R-C-L circuit. Because the difference between X_L and X_c is squared, the order in which the quantities are subtracted does not affect the answer.

Example: Find the impedance of a series R-C-L circuit, when R = 6 , X_L = 20 , and X_c = 10 (Figure 9).

Figure 9 Simple R-C-L Circuit

Solution:

Impedance in a parallel R-C-L circuit equals the voltage divided by the total current. Equation (8-14) is the mathematical representation of the impedance in a parallel R-C-L circuit.

where

Total current in a parallel R-C-L circuit is equal to the square root of the sum of the squares of the current flows through the resistance, inductive reactance, and capacitive reactance branches of the circuit. Equations (8-15) and (8-16) are the mathematical representations of total current in a parallel R-C-L circuit. Because the difference between I_L and I_c is squared, the order in which the quantities are subtracted does not affect the answer.

where

Example:

A 200 resistor, a 100 X_L,and an 80 X_c are placed in parallel across a 120V AC source (Figure 10). Find: (1) the branch currents, (2) the total current, and (3) the impedance.

Figure 10 Simple Parallel R-C-L Circuit

Solution:

Summary

Impedance is summarized below.

Impedance Summary

Impedance (Z) is the total opposition to current flow in an AC circuit. The formula for impedance in a series AC circuit is:

The formula for impedance in a parallel R-C-L circuit is:

The formulas for finding total current (I_T) in a parallel R-C-L circuit are: