RLC Resonance Calculator
A series RLC circuit with 10 mH and 1 µF resonates at 1591.55 Hz, with Q = 10 and a bandwidth of 159 Hz for R = 10 Ω.
1591.54943091895 Hz
Full answer, then cut to fewer decimals (not rounded):
- 1591.54943091895 Hz
- 1591.5494309189 Hz
- 1591.549430918 Hz
- 1591.54943091 Hz
- 1591.5494309 Hz
- 1591.549430 Hz
- 1591.54943 Hz
- 1591.5494 Hz
- 1591.549 Hz
- 1591.54 Hz
- 1591.5 Hz
- Angular frequency ω₀
- 10000 rad/s
- Quality factor Q
- 10
- Bandwidth f₀/Q
- 159.1549431 Hz
- Lower half-power frequency
- 1513.960154 Hz
- Upper half-power frequency
- 1673.115097 Hz
- Damping ratio ζ
- 0.05
- Step response
- underdamped, ringing at ω_d = 9987.49 rad/s
- Impedance at resonance (= R, minimum)
- 10 Ω
Step-by-step solution
- f₀ = 1 ÷ (2π √(LC)) = 1 ÷ (2π √(0.01 × 0.000001)) = 1591.549431 Hz
- Q = (1/R) √(L/C) = (1/10) × √(0.01 ÷ 0.000001) = 10
- ζ = 1 ÷ 2Q = 0.05 (underdamped)
RLC Resonance Formula
f₀ = 1 / (2π√(LC)), Q = (1/R)√(L/C) (series)
parallel: Q = R√(C/L); bandwidth = f₀/Q; ζ = 1/(2Q)
Worked Example
A series circuit with R = 10 Ω, L = 10 mH and C = 1 µF:
- f₀ = 1 ÷ (2π √(LC)) = 1 ÷ (2π √(0.01 × 0.000001)) = 1591.549431 Hz
- Q = (1/R) √(L/C) = (1/10) × √(0.01 ÷ 0.000001) = 10
- ζ = 1 ÷ 2Q = 0.05 (underdamped)
Quality factor Q: 10 · Bandwidth f₀/Q: 159.1549431 Hz · Lower half-power frequency: 1513.960154 Hz · Upper half-power frequency: 1673.115097 Hz · Damping ratio ζ: 0.05 · Step response: underdamped, ringing at ω_d = 9987.49 rad/s · Impedance at resonance (= R, minimum): 10 Ω
GATE tip
In a series RLC circuit at resonance, the voltage across L (or C) is Q times the supply voltage. With Q = 10 and 10 V applied, 100 V appears across the capacitor, a favourite GATE trap.
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Frequently asked questions
What happens at resonance?
The inductive and capacitive reactances are equal and cancel. A series circuit then has its minimum impedance (just R) and maximum current; a parallel circuit has its maximum impedance.
How are Q and damping related?
ζ = 1/(2Q). Q above 0.5 means underdamped: the circuit rings after a step. Q = 0.5 is critical damping.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). RLC Resonance Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/rlc-resonance-calculator/
IEEE
Scientific Converters, "RLC Resonance Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/rlc-resonance-calculator/