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Electricity

RLC Circuit Calculator

Analyze series RLC circuits: impedance, current, voltage drops, resonant frequency, quality factor, and bandwidth.

Interactive calculator

RLC Circuit Calculator

Calculate series RLC impedance, current and voltage drops, resonant frequency, Q factor, and bandwidth.

Total series resistance

Inductor value

Capacitor value

AC signal frequency

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose a mode: impedance, current & voltage drops, resonance, or Q & bandwidth.
  • Enter R, L, C, and frequency as needed.
  • Click Calculate for detailed results.

Table of Contents

Key Takeaways

  • A series RLC circuit has resistance, inductance, and capacitance in one loop.
  • Impedance Z = √(R² + (XL − Xc)²) combines resistance and net reactance.
  • At resonance (f₀ = 1/(2π√LC)), XL = Xc and impedance equals R alone.
  • The quality factor Q = (1/R)√(L/C) measures circuit selectivity.
  • Bandwidth BW = f₀/Q gives the frequency range between −3 dB points.

What Is an RLC Circuit?

An RLC circuit contains a resistor, inductor, and capacitor. In the series configuration, all three components share the same current. The circuit exhibits frequency-dependent impedance, resonance, and can act as a bandpass or band-stop filter depending on where the output is measured.

RLC Circuit Infographic

RLC Circuit Formulas

Z=R2+(XL−XC)2Z = \sqrt{R^2 + (X_L - X_C)^2}

Series impedance magnitude

f0=12πLCf_0 = \frac{1}{2\pi\sqrt{LC}}

Resonant frequency

Q=1RLCQ = \frac{1}{R}\sqrt{\frac{L}{C}}

Quality factor

BW=f0QBW = \frac{f_0}{Q}

Bandwidth (\u22123 dB)

Resonance in RLC Circuits

At resonance, the inductive and capacitive reactances cancel (XL = Xc), leaving only resistance. This means maximum current flows, minimum impedance, and zero phase angle. The voltage across L and C can individually exceed the source voltage by a factor of Q.

Quality Factor (Q)

The Q factor describes how underdamped the circuit is. High Q (>10) means sharp resonance and narrow bandwidth, useful for radio tuning. Low Q (<1) means the circuit is overdamped with broad frequency response. Q also equals the voltage magnification factor at resonance: VL = VC = Q × Vs.

How to Use the RLC Circuit Calculator

  1. 1Select a calculation mode from the dropdown.
  2. 2Enter resistance, inductance, capacitance, and/or frequency.
  3. 3For current mode, also enter the source voltage (RMS).
  4. 4Click Calculate to see impedance, phase, Q, and more.
  5. 5Review the step-by-step solution and explanation.

Example Calculations

Series Impedance

R = 10 Ω, L = 100 mH, C = 10 μF, f = 100 Hz. XL = 62.83 Ω, Xc = 159.15 Ω. |Z| = √(100 + 9270) ≈ 96.89 Ω. Circuit is capacitive.

Resonant Frequency

L = 100 mH, C = 10 μF. f&sub0; = 1/(2π√(0.1 × 10−5)) ≈ 159.15 Hz.

Q Factor

R = 10 Ω, L = 100 mH, C = 10 μF. Q = (1/10)√(0.1/10−5) = 10. BW = 159.15/10 = 15.92 Hz.

Where RLC Circuit Calculations Are Used

Radio tuning circuits, bandpass filters, antenna matching, oscillators, signal processing, power factor correction, notch filters, and educational physics and EE courses.

Common Mistakes

  • Forgetting that XL and Xc subtract (not add) in series.
  • Confusing series and parallel RLC formulas.
  • Using peak voltage when RMS is required.
  • Not converting mH to H or μF to F.
  • Expecting voltage drops to add algebraically (they add as phasors).

Accuracy and Limitations

This calculator uses ideal RLC equations. Real inductors have winding resistance, real capacitors have ESR, and parasitic effects become significant at high frequencies. Mutual coupling and non-linear cores are not modeled. For precision work, use SPICE simulation.

Frequently Asked Questions

What is an RLC circuit?›

An RLC circuit contains a resistor (R), inductor (L), and capacitor (C). In a series RLC circuit, these three components are connected in one loop. The interplay of resistance, inductive reactance, and capacitive reactance determines the circuit’s frequency response.

What happens at resonance?›

At the resonant frequency, inductive reactance equals capacitive reactance (XL = Xc). The impedance drops to its minimum value R, current is maximized, and the circuit behaves as a purely resistive load.

What is the Q factor?›

The quality factor Q measures how sharp the resonance peak is. Higher Q means narrower bandwidth and greater frequency selectivity. Q = (1/R)√(L/C) for a series RLC circuit.

What is bandwidth in an RLC circuit?›

Bandwidth (BW) is the frequency range between the upper and lower −3 dB points. BW = f₀/Q. A higher Q gives a narrower bandwidth.

Can voltage across L or C exceed the source?›

Yes! At resonance in a series RLC circuit, VL and VC can each be Q times the source voltage. This voltage magnification is a key property of resonant circuits.

What is the difference between series and parallel RLC?›

In a series RLC, components share the same current and impedance is minimized at resonance. In a parallel RLC, components share the same voltage and impedance is maximized at resonance. This calculator covers series RLC.

How do I determine if a circuit is inductive or capacitive?›

If XL > Xc, the circuit is inductive (positive phase angle, voltage leads current). If Xc > XL, it is capacitive (negative phase angle, current leads voltage).

Does resistance affect resonant frequency?›

No. The resonant frequency f₀ = 1/(2π√LC) depends only on L and C. However, R affects the Q factor, bandwidth, and the sharpness of the resonance peak.

Sources / References

  1. OpenStax University Physics Vol 2: RLC Circuits
  2. HyperPhysics: RLC Circuits
  3. NIST: SI Units
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish