Impedance (RLC Series)

Formula

Description

Impedance is the AC equivalent of resistance and represents the total opposition to alternating current in a circuit containing resistance and reactance. It is calculated as the magnitude of the complex impedance vector Z = R + j(XL - XC), where resistance forms the real component and net reactance forms the imaginary component. The Pythagorean relationship arises because resistance and reactance are orthogonal in the phasor domain: resistive voltage is in phase with current while reactive voltage is 90 degrees out of phase. When XL equals XC the circuit is at resonance and impedance equals pure resistance.

Variables

• Z — Impedance magnitude in ohms (Ω)
• R — Resistance in ohms (Ω)
• XL — Inductive reactance in ohms (Ω)
• XC — Capacitive reactance in ohms (Ω)

Practical Notes

The phase angle of impedance is arctan((XL - XC) / R). Positive angles indicate net inductive behavior (current lags voltage), negative angles indicate net capacitive behavior (current leads voltage). Impedance matching is critical in RF design to maximize power transfer.