Electrical
RLC Circuit
Resistor, inductor, and capacitor combining to form resonant systems
An RLC circuit contains resistance (R), inductance (L), and capacitance (C). At a specific resonant frequency, inductive and capacitive reactances cancel, leaving only resistance to limit current. Series RLC circuits exhibit minimum impedance at resonance; parallel RLC circuits exhibit maximum impedance. The quality factor Q describes how sharply the circuit selects its resonant frequency, balancing energy storage against dissipation. RLC circuits are the backbone of radio tuning, oscillators, filters, and any system where frequency selectivity matters.
- Resonant frequencyf_0 = 1 / (2π√(LC))
- Series impedance minZ = R at resonance
- Quality factorQ = ω_0 L / R
- BandwidthBW = f_0 / Q
- DampingUnderdamped, critical, overdamped
- Used inRadios, filters, oscillators
Interactive visualization
Press play, or step through manually. The visualization is yours to drive — try it before reading on.
Watch the 60-second explainer
A condensed visual walkthrough — narrated, captioned, under a minute.
Why RLC circuits matter
- Radio. Tuning circuits in every receiver and transmitter.
- Oscillators. Generating clean sine waves for clocks and carriers.
- Filters. Bandpass, band-stop, lowpass, highpass topologies.
- Power conditioning. Smoothing supplies, suppressing transients.
- Wireless charging. Resonant inductive coupling.
- Sensors. Frequency-shift detection of metal, moisture, capacitance.
- EMI suppression. Notching out interference at known frequencies.
Common misconceptions
- Resonance is always desirable. Unintended resonances cause failures and noise.
- Q is always high. Heavily damped circuits have Q under 1 by design.
- Inductors store charge. They store energy in magnetic field, not charge.
- Voltage can't exceed source. At resonance, L and C voltages can be Q× larger.
- R only dissipates. Parasitic R sets bandwidth and ultimate Q.
- Series and parallel are interchangeable. Their behaviors at resonance are inverse.
Frequently asked questions
What's the resonant frequency?
f_0 = 1 / (2π√(LC)). At this frequency, the inductor's reactance (ωL) equals the capacitor's reactance (1/ωC), and they cancel because they're 180° out of phase. Only resistance remains. In a series circuit this means maximum current; in a parallel tank, minimum current from the source.
What's the quality factor?
Q = ω_0 L / R for a series circuit, or R/(ω_0 L) for parallel. It quantifies how sharply the circuit resonates. High Q means narrow bandwidth and high voltage buildup at resonance, but slow response to changes. Low Q means broad bandwidth, fast response, and modest peak. Radio tuners need Q around 100; a damped suspension wants Q under 1.
What's the difference between series and parallel?
Series RLC: components on a single loop. Impedance is minimum at resonance (just R), so current peaks. Parallel RLC: components across the same two nodes. Impedance is maximum at resonance (a tank circuit), so current from the source dips. Both ring at the same f_0, but their roles in filters differ.
How does it select a radio station?
Antenna picks up many frequencies. An RLC tank tuned to the desired f_0 presents high impedance only at that frequency, allowing it to develop voltage while shorting other frequencies through the inductor. A variable capacitor (or varactor diode) tunes f_0 by changing C. Higher Q means better selectivity but harder tuning.
What's damping?
How quickly oscillations die out. Underdamped: oscillates at ringing frequency, slowly decaying. Critically damped: returns to equilibrium fastest without oscillation. Overdamped: returns slowly without oscillation. The damping ratio ζ = R/(2√(L/C)) determines behavior. Suspension systems target slightly underdamped (around ζ = 0.7) for fast response without bounce.
How is it used in filters?
Many configurations. Series RLC across a load forms a band-stop (notch) filter, blocking f_0. Parallel RLC across a load forms a bandpass, allowing only f_0. Cascading multiple sections gives sharper rolloffs. Audio crossovers in speakers, intermediate frequency stages in receivers, and EMI suppressors all use RLC topologies.
What's resonance overshoot?
At resonance in a high-Q circuit, the voltage across L and C individually can far exceed the source voltage. With Q=100, the capacitor sees 100× the input voltage. This is exploited in Tesla coils and induction heaters but causes failures if components aren't rated for the buildup. Fuses and overvoltage protection are essential in high-Q power circuits.