RLC Circuit Solver Calculator

Solve RLC behavior fast with clear numeric outputs. Compare series and parallel responses across frequencies. Download reports, validate units, and study resonance safely today.

Inputs
Enter values, choose scaling, then press Solve.
Circuit type affects impedance and Q approximations.

Series: Z = R + j(ωL − 1/ωC). Parallel: Z = 1/(1/R + j(ωC − 1/ωL)).
Amplitude is peak value, not RMS.
Angular frequency ω = 2πf.
Advanced: Plot sweep settings
Blank uses about 0.2×f0.
Blank uses about 5×f0.
Clamped to 10–500, log spaced.
Reset
After solving, use CSV/PDF buttons above the form.

Example Data Table

Circuit R (Ω) L (H) C (F) f (Hz) f0 (Hz) |Z| (Ω) Irms (A)
Series 10 0.05 1e-6 1000 712.38 41.21 0.0858
Series 2 0.01 4.7e-6 800 734.86 3.54 0.999
Parallel 1000 0.02 1e-6 500 1125.40 780.42 0.0045
Values above are illustrative and may differ with rounding.

Formulas Used

Steady-state AC
  • ω = 2πf
  • f0 = 1 / (2π√(LC))
  • Zseries = R + j(ωL − 1/(ωC))
  • Yparallel = 1/R + j(ωC − 1/(ωL))
  • Zparallel = 1 / Yparallel
  • |Z| = √(Re(Z)² + Im(Z)²)
  • ∠Z = atan2(Im(Z), Re(Z))
  • |I| = V / |Z|, Irms = |I|/√2
  • Pseries = Irms²·R, Pparallel ≈ Vrms²/R
Second-order dynamics (series model)
  • ω0 = 1/√(LC)
  • α = R/(2L)
  • ζ = (R/2)√(C/L)
  • ωd = ω0√(1 − ζ²) if ζ < 1
  • Qs = (1/R)√(L/C) (series)
  • Qp ≈ R√(C/L) (parallel, high-Q)
  • Bandwidth ≈ f0/Q
Parallel Q is an approximation that improves for high resistance and narrow bandwidth.

How to Use This Calculator

  1. Select Series or Parallel RLC configuration.
  2. Enter R, L, C, voltage amplitude, and frequency.
  3. Use unit scaling menus for kΩ, mH, µF, and more.
  4. Press Solve RLC to compute resonance and impedance.
  5. Review KPIs, then expand the full result list.
  6. Use Download CSV or Download PDF to export.

Input ranges and measurement context

RLC solvers perform best when values match real measurement scales. Common bench parts include resistors from 1 to 10000 ohms, inductors from 1 microhenry to 10 henry, and capacitors from 1 picofarad to 10 millifarad. Measure R with a meter, and confirm L and C at the test frequency, because datasheets quote 1 kHz values.

Resonance and bandwidth interpretation

The resonant frequency f0 = 1/(2π√(LC)) links energy exchange between L and C. Around f0, series circuits show minimum impedance magnitude and maximum current, while parallel circuits show maximum impedance magnitude and minimum supply current. Bandwidth is estimated as BW ≈ f0/Q, so a 1 kHz circuit with Q = 20 has BW near 50 Hz.

Damping classification in time response

The damping ratio ζ indicates whether oscillations appear after a step or impulse in a series model. ζ below 1 produces ringing at ωd = ω0√(1−ζ²), ζ equal 1 returns fastest non oscillatory settling, and ζ above 1 yields slower non oscillatory decay. The attenuation α = R/(2L) sets the exponential envelope; doubling R doubles α and shortens the decay constant.

Power and phase behavior

Real power depends on resistive loss. For series, P = Irms²R; for parallel, P ≈ Vrms²/R. Phase angle tracks reactive dominance: negative phase suggests capacitive behavior, positive phase suggests inductive behavior, and near zero phase indicates near resonant operation. At resonance, the reactive terms cancel, yet component voltages can exceed the source by roughly Q times in high selectivity designs.

Quality factor as selectivity metric

Q compresses frequency selectivity into one number. For series, Qs = (1/R)√(L/C); for parallel (high Q), Qp ≈ R√(C/L). Higher Q increases peak response near resonance but reduces bandwidth and increases sensitivity to tolerances. With 5 percent L and 5 percent C, f0 can shift by about 5 percent, so verify margins in filters and oscillators.

Frequency sweep visualization guidance

A sweep plot reveals how impedance, current, and phase evolve across frequency. Set the sweep to span at least 0.2×f0 to 5×f0 for clear curvature. Use more points for high Q circuits where peaks are narrow; 200 points is a default. Export CSV or PDF to document design iterations, compare revisions, and share with reviewers.

FAQs

1) What does the solver compute after I press Solve?

It calculates resonance, impedance magnitude, phase angle, current, estimated Q, bandwidth, damping ratio, and real power using your selected series or parallel model and the entered units.

2) Why does the parallel Q look different from series Q?

Series Q uses loss in R along the current path. Parallel Q here uses a high‑Q approximation based on shunt resistance. For low resistance or wide bandwidth, treat the parallel Q as a guideline.

3) Can I use RMS voltage instead of amplitude?

Enter peak amplitude. If you only know RMS, multiply by √2 before input. The solver reports Irms directly, so power estimates align with standard AC calculations.

4) What frequency sweep should I choose for the plot?

Start near 0.2×f0 and end near 5×f0 for most designs. For high selectivity, increase points so the peak is smooth and the phase transition is well resolved.

5) What happens if I set R to zero?

Ideal zero resistance removes damping and makes Q undefined. The solver will still compute reactance‑based impedance, but power and bandwidth outputs may show N/A because real losses are not represented.

6) Is this suitable for safety‑critical designs?

Use it for analysis and documentation, then validate with component tolerances, parasitics, and measurements. For critical hardware, confirm results with simulation tools and verified lab data.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.