How this calculation works
Normalize component units, identify the free-response regime and show a damped oscillation frequency only below critical resistance. Zero series resistance has an ideal infinite quality factor, shown as text.
ω0 = 1/√(LC); α = R/(2L); ζ = α/ω0; Rcritical = 2√(L/C)A worked example
100 mH and 10 µF give an undamped natural frequency about 159.154943 Hz. At 10 Ω, damping ratio is 0.05 and critical series resistance is 200 Ω; the damped free-oscillation frequency is slightly lower.
Good to know
An ideal lumped series RLC free-response model. No driven voltage-gain peak, initial-condition waveform, parasitic or saturation model. ESR and winding resistance are not inferred, and no component ratings are selected.
Reference: Reference: model definitions and scope (opens in a new tab) ↗
Natural frequency and damped oscillation frequency are distinct
For 100 mH and 10 µF, the undamped natural angular frequency is 1,000 rad/s, or about 159.154943 Hz. Adding 10 Ω gives a decay coefficient of 50 per second and damping ratio 0.05. The free oscillation frequency is slightly below the undamped natural frequency.
The undamped frequency depends on L and C, while series resistance changes damping. A free-response oscillation frequency should not be substituted for every possible driven resonance or voltage-gain peak. This page does not sweep an external driving frequency or solve a filter transfer curve.
The RL transient calculator describes a different first-order loop. A series RLC model adds a second energy-storage element and can have an oscillatory free response.
Critical resistance divides oscillatory and non-oscillatory cases
The default critical series resistance is 200 Ω. Below that value the ideal free response oscillates with decay; at the critical value it is non-oscillatory, and larger resistance gives an overdamped free response. The table expresses resistance as a fraction of the critical value while keeping L and C fixed.
At zero series resistance, this ideal model has no resistive decay and an infinite quality factor. Infinity is reported as a description rather than a finite numeric measurement. It does not assert that a real coil, capacitor and connection have no losses.
The resistance boundary belongs to the complete modeled series loop
The entered R should represent the series resistance you intend to include. The calculator does not look up coil resistance or capacitor ESR. Changing inductance or capacitance units also requires keeping the numerical inputs consistent with their new interpretation.
The capacitor series and parallel network calculator can find a separate ideal equivalent before it is used in another model. The RL current growth and decay calculator has one energy-storage element instead of two. This RLC page does not specify initial charge/current, produce a waveform or determine physical operating limits.
A few questions, answered
Does increasing R change the undamped natural frequency?
Not with L and C fixed. It changes the damping parameters and whether the free response oscillates.
Why is the damped frequency absent at or above critical resistance?
The ideal free response is non-oscillatory there, so an oscillation frequency is not applicable.
Does zero R mean a measured infinite Q?
No. It is the lossless idealization. Real losses are not inferred.
Is this a driven gain or resonance-peak calculator?
No. It reports natural and free-response damping parameters for a series RLC model.