Definition

Reactance

X_{L} = ω L, X_{C} = \frac{1}{ω C}

Statement

Inductive and capacitive reactance — the frequency-dependent counterparts of resistance for an inductor and a capacitor.

Symbols and units

$X_{L}, X_{C}$	inductive, capacitive reactance	Ω
$ω$	angular frequency	rad/s
$L, C$	inductance, capacitance	H, F

When it applies

Ideal inductors and capacitors driven by a sinusoidal source at angular frequency ω.

Don't use when

Defined for ideal inductors and capacitors driven by a sinusoidal source — a non-sinusoidal drive requires Fourier decomposition into sinusoidal components first.

Derivation

Reactance is defined analogously to resistance, V_max = I_max X, but its value depends on frequency because it comes from the calculus of a sinusoidal current through L or C rather than from a fixed material property.

X_{L} = ω L, X_{C} = \frac{1}{ω C}

Worked examples

Reactance at the extremes of frequency

ω \to 0 : X_{L} \to 0, X_{C} \to \infty ω \to \infty : X_{L} \to \infty, X_{C} \to 0

At DC, an inductor behaves like a plain wire and a capacitor like an open circuit — the opposite of their behaviour at very high frequency.

Watch out for

Inductive reactance GROWS with frequency; capacitive reactance SHRINKS with frequency — opposite trends, the basis of every filter circuit. As ω → 0 (DC), X_L → 0 (an inductor is a short) and X_C → ∞ (a capacitor is an open circuit).