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Reactance and Impedance

In AC circuits, capacitors and inductors get a frequency-dependent opposition to current called reactance. The reactance of an inductor increases with frequency, while the reactance of a capacitor decreases. Together with the ordinary resistance, the reactance forms the impedance, which sets both the current's magnitude and its phase shift.

X_L=\omega L

inductive reactance

X_C=\dfrac{1}{\omega C}

capacitive reactance

Z=\sqrt{R^2+X^2},\ \varphi=\arctan\dfrac{X}{R}

impedance magnitude and phase angle

Symbols

$X_L,\ X_C$	reactance (inductor, capacitor)	$\Omega$
$Z$	impedance	$\Omega$
$\varphi$	phase angle	°

Example

$R=30$ Ω, $X_L=31.4$ Ω:

$Z=\sqrt{30^2+31.4^2}\approx43.4$ Ω.

X_C

decreases as frequency rises, while

X_L

increases – they behave oppositely.

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