How to use the RLC Resonance Calculator
- 1. Pick the circuitSeries RLC, parallel RLC, or a tank with R in series with L.
- 2. Enter R, L and CPrefixes work: 10m, 1u, 4.7k.
- 3. Read the resultsf₀, Q, BW, f₁, f₂, |Z| plot and the working.
Resonance formulas
At resonance the inductive and capacitive reactances are equal: ω₀L = 1/(ω₀C), so ω₀ = 1/√(LC) and f₀ = 1/(2π√(LC)). In a series circuit, Z = R is a minimum and Q = ω₀L/R = (1/R)√(L/C). In a parallel circuit, Z = R is a maximum and Q = R√(C/L). Bandwidth = f₀/Q, and the exact half-power frequencies come from ω = ∓α + √(α² + ω₀²) with α = R/2L (series) or 1/2RC (parallel). A practical tank resonates at ω₀ = √(1/LC − R²/L²) with dynamic impedance L/(CR).
Worked example: R = 10 Ω, L = 10 mH, C = 1 µF in series gives ω₀ = 10,000 rad/s, f₀ = 1.592 kHz, Q = 100/10 = 10 and BW = 159.2 Hz. A 1 V supply then puts 10 V across both L and C.
Exam tips
- The series RLC is an acceptor circuit (minimum Z, maximum current). The parallel RLC is a rejector circuit (maximum Z, minimum line current).
- f₀ ± BW/2 is only an approximation for high Q. The tool gives the exact f₁ and f₂.
- Voltage magnification in series is Q (VL = VC = QV). Current magnification in parallel is also Q.
- Damping ratio ζ = 1/(2Q) links resonance to transient response.
Frequently asked questions
What is the difference between series and parallel resonance?
At series resonance the impedance is a minimum (R) and current is a maximum. At parallel resonance the impedance is a maximum and the line current is a minimum. Both happen at f₀ = 1/(2π√LC) in the ideal case.
Why does the tank circuit give a lower resonant frequency?
The coil resistance shifts the point where the circuit looks purely resistive: ω₀ = √(1/LC − R²/L²). If R > √(L/C), there is no resonance at all.
Is bandwidth in Hz or rad/s?
The tool shows bandwidth in Hz. Multiply by 2π for rad/s.
Is this tool free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. All the maths runs in your browser.