**Impedance in R-L-C Circuit.**

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 XL and Xc 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 , XL = 20 , and Xc = 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 IL and Ic is squared, the order in which the quantities are subtracted does not affect the answer.

where

Example:

A 200 resistor, a 100 XL,and an 80 Xc 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 (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 (IT) in a parallel R-C-L circuit are: