A coil, a capacitor and a resistor wired in a loop and driven by an AC source. Sweep the drive frequency: does the circuit respond the same at every frequency, or does it 'prefer' one — and if so, what sets it?
▶ Launch the interactive simulationDrive a series RLC loop with V₀cos ωt, so the charge obeys L q̈ + R q̇ + q/C = V₀cos ωt — the driven damped oscillator with L↔mass, 1/C↔stiffness, R↔friction. The lab sweeps the drive frequency through ω₀ and traces the steady current amplitude |I|(ω), shading the half-power band, while the live coil (½LI²) and capacitor (q²/2C) hand the energy back and forth. A real AM-radio tank — L=250 µH, C=100 pF, R=10 Ω — is swept with ±1.5% reading noise on the peak.
There IS a preferred frequency: the current amplitude |I| = V₀/√(R²+(ωL−1/ωC)²) peaks SHARPLY at the natural frequency ω₀ = 1/√(LC), where the inductive and capacitive reactances cancel and the loop looks like a bare resistor (|I| = V₀/R). The sharpness is the quality factor Q = (1/R)√(L/C) = ω₀/Δω, and the current's phase flips from leading (below ω₀) to lagging (above) through resonance. Reading a real tank recovers f₀ ≈ 1.01 MHz, Q ≈ 158 and (with C known) L ≈ 250 µH; its 6 kHz bandwidth is narrower than the 10 kHz station spacing — which is exactly how a radio dial picks one station out of the air