Result

LC oscillation frequency

ω = \frac{1}{L C}

Statement

The natural angular frequency at which charge and current oscillate in an ideal LC circuit.

Symbols and units

$ω$	natural angular frequency	rad/s
$L$	inductance	H
$C$	capacitance	F

When it applies

An ideal LC circuit with zero resistance.

Don't use when

Assumes an ideal LC circuit with zero resistance — any real resistance damps the oscillation and shifts the frequency slightly (see RLC resonance instead).

Derivation

The loop rule for L and C in series gives the same differential equation as simple harmonic motion, with charge playing the role of position:

L \frac{d ^{2} q}{d t ^{2}} + \frac{q}{C} = 0 \Rightarrow ω = \frac{1}{L C}

Watch out for

Charge and current oscillate exactly like position and velocity in SHM — energy sloshes between the capacitor's electric field and the inductor's magnetic field, with no resistance present to damp it.

Connects to

Simple harmonic motion