Result

Resonance frequency

(E11.4.1) E11.4 · Resonance and Transformers →

ω_{0} = \frac{1}{L C}

Statement

The driving frequency at which impedance is minimized (Z = R alone) and current is maximized.

Symbols and units

$ω_{0}$	resonance angular frequency	rad/s
$L, C$	inductance, capacitance	H, F

When it applies

A series RLC circuit; resonance occurs at the same frequency the undriven LC circuit would oscillate at.

Don't use when

Specific to a series RLC circuit — a parallel RLC circuit resonates at a current minimum instead of a maximum.

Derivation

Impedance is minimized when the reactances cancel exactly, X_L = X_C — precisely the frequency at which an undriven LC circuit would oscillate on its own:

ω L = \frac{1}{ω C} \Rightarrow ω_{0} = \frac{1}{L C}

Watch out for

At resonance, current is maximum, but the voltage across L and C individually can be far LARGER than the source voltage — energy sloshes between them with only R limiting how large it grows.

Connects to

LC oscillation frequency