Adding resistance to an LC circuit damps its oscillations. The quality factor Q measures how sharp the resonance is: high-Q circuits pick out a narrow band of frequencies, low-Q circuits respond broadly.
How to use the RLC Circuit Calculator
- Circuit
- Resistance R
- Inductance L
- Capacitance C
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose series or parallel and enter R, L and C.
Inputs explained
| Field | What to enter |
|---|---|
| Circuit | Choose one: Series RLC, Parallel RLC |
| Resistance R | Units: Ω, kΩ, MΩ, mΩ |
| Inductance L | Units: mH, µH, nH, H |
| Capacitance C | Units: nF, µF, pF, mF, F |
What each result means
- Resonant frequency f₀ = 1÷(2×pi×sqrt([Inductance L]×[Capacitance C]))
- Bandwidth = 1÷(2×pi×sqrt([Inductance L]×[Capacitance C]))÷[Quality factor Q]
- Damping ratio ζ = 1÷(2×[Quality factor Q])
Example values
How the main result changes when Resistance R changes and everything else stays at the example values above:
| Resistance R (Ω) | Resonant frequency f₀ (Hz) |
|---|---|
| 5 | 15,915.4943 |
| 7.5 | 15,915.4943 |
| 10 | 15,915.4943 |
| 12.5 | 15,915.4943 |
| 15 | 15,915.4943 |
| 20 | 15,915.4943 |
Formula
f₀ = 1/(2π√(LC)) · Series: Q = (1/R)·√(L/C) · Parallel: Q = R·√(C/L) · BW = f₀/Q
Worked example
Inputs — Circuit: Series RLC; Resistance R: 10 Ω; Inductance L: 1 mH; Capacitance C: 100 nF.
Results — Resonant frequency f₀ = 15,915.49431 Hz; Quality factor Q = 10; Bandwidth = 1,591.54943 Hz; Damping ratio ζ = 0.05; Response = Underdamped (rings).
Key terms
- Damping ratio
- ζ = 1/(2Q).
Frequently asked questions
What is the Q factor?
Resonant frequency divided by bandwidth.
Why does Q differ between series and parallel?
Resistance damps them in opposite ways.
What happens with very low Q?
The circuit no longer oscillates (overdamped).
Where are RLC circuits used?
Filters, tuners, oscillators and impedance matching.