Result

Impedance of a series RLC circuit

Z = R^{2} + (X_{L} - X_{C})^{2}

Statement

The total opposition to current in a series RLC circuit, combining resistance and net reactance.

Symbols and units

$Z$	total impedance	Ω
$R$	resistance	Ω
$X_{L}, X_{C}$	inductive, capacitive reactance	Ω

When it applies

A series RLC circuit driven by a sinusoidal source.

Don't use when

Not simply R + X_L + X_C — the reactances partially cancel before combining with resistance via the Pythagorean formula.

Derivation

X_L and X_C are 180° out of phase with each other in the phasor diagram (opposite in sign), so they partially cancel before combining with R at 90°:

Z = R^{2} + (X_{L} - X_{C})^{2}

Watch out for

Impedance is not simply R + X_L + X_C — the reactances partially cancel before the Pythagorean combination with resistance.

Connects to