🔌 RLC Circuit — Resonance & Oscillations
A series RLC circuit obeys L d²Q/dt² + R dQ/dt + Q/C = Vs. At resonance ω₀ = 1/√(LC) the impedance is purely resistive and current peaks. Adjust R, L, C to explore underdamped oscillations, critical damping and the Q-factor.
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What this demonstrates
The RLC series circuit is the electrical analogue of a mass-spring-damper system. Charge Q on the capacitor plays the role of displacement, current I = dQ/dt is velocity, and the inductor stores magnetic energy like a mass stores kinetic energy. The circuit oscillates at ω₀ = 1/√(LC) when under-damped (R < 2√(L/C)). The Q-factor (quality factor) = ω₀L/R determines both the sharpness of the resonance peak and the number of oscillations before decay.
How to use
- Free mode: watch natural decaying oscillations of Q(t) and I(t)
- Driven mode: sweep the driving frequency — notice amplitude peaks at ω₀
- Decrease R to sharpen the resonance (higher Q) and slow the decay
- The impedance curve Z(ω) = √(R² + (ωL − 1/ωC)²) shows the minimum at ω₀
Did you know?
RLC circuits are at the heart of radio tuning: your phone's antenna circuit is an RLC resonator whose C (or L) is adjusted to pick the exact carrier frequency. The Q-factor of a high-quality quartz crystal oscillator can exceed 100 000, enabling the precision timing in GPS receivers and atomic clocks.