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LC Circuit Resonant Frequency Calculator

Solve for resonant frequency, inductance, or capacitance in an LC tank circuit via f = 1 ÷ (2π√(LC)), plus angular frequency and characteristic impedance.

Resonant frequency (f₀)
503.2921 Hz
Inductance
10 mH
Capacitance
10 µF
Angular frequency (ω)
3,162.2777 rad/s
Characteristic impedance (Z₀)
31.6228 Ω

How it works

An inductor and capacitor wired together form a 'tank' circuit that naturally oscillates at the frequency where the inductor's and capacitor's opposing reactances cancel out: f = 1 ÷ (2π√(LC)), with inductance in henries and capacitance in farads. Given any two of {frequency, inductance, capacitance}, this calculator rearranges that same identity to solve for whichever one you leave as the target — inductance and capacitance are entered in the practical units real components are labeled in (mH and µF) and converted internally before the formula runs.

Two related figures are reported alongside the resonant frequency: angular frequency ω = 2πf (radians per second, the form the underlying differential equation is naturally expressed in) and characteristic impedance Z₀ = √(L/C) (ohms), the impedance the inductor and capacitor each present at resonance.

The default values, 10 mH and 10 µF, resonate at about 503.3 Hz — a commonly cited reference pair for sanity-checking this exact formula.

FAQ

What does an LC circuit's resonant frequency actually mean physically?

At resonance, energy sloshes back and forth between the inductor's magnetic field and the capacitor's electric field with no net reactive opposition to current flow — it's the same kind of natural back-and-forth as a pendulum or a mass on a spring, just in an electrical rather than mechanical system. Below resonance the capacitor's reactance dominates; above it, the inductor's does.

Does this account for the circuit's own resistance?

No — this models the idealized, lossless LC resonance taught in circuit theory. A real inductor's winding resistance (and any other resistance in the loop) damps the oscillation and, in a driven RLC circuit, slightly shifts and broadens the resonance peak — effects this calculator doesn't include.

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