Last updated: 2026-06-16

RLC Impedance

A series RLC circuit places a resistor, an inductor and a capacitor in line with an AC source. Each element opposes the current differently: the resistor by resistance, the inductor by inductive reactance, and the capacitor by capacitive reactance. The combined opposition is called impedance. This calculator takes the resistance $R$, frequency $f$, inductance $L$ and capacitance $C$ and returns the impedance $Z$, the phase angle, and both reactances.

Formula

The two reactances subtract because the inductor and capacitor push the current in opposite directions. When $X_L > X_C$ the net reactance is inductive and $\varphi$ is positive; when $X_C > X_L$ it is capacitive and $\varphi$ is negative.

Worked example

Take $R = 100\ \Omega$, $f = 1\ \text{kHz}$, $L = 10\ \text{mH}$ and $C = 1\ \mu\text{F}$.

The negative phase angle shows the circuit is capacitive at this frequency, because $X_C$ is larger than $X_L$.

Reactances across frequency

For $L = 10\ \text{mH}$ and $C = 1\ \mu\text{F}$:

Why it matters

Impedance determines how much current flows for a given AC voltage and how voltage and current line up in time. Series RLC circuits are the building blocks of tuned filters, oscillators and radio front ends. At resonance the reactances cancel, the impedance falls to just $R$, and the current peaks — the property that lets a receiver select one station out of many.