NapkinCalc

Electricity 2 — AC Circuits

Resonance

continues from lesson 3 — values defined earlier in the course stay live here

ELI5: sweep the frequency and there's exactly one spot where X_L = X_C — they cancel, impedance collapses to just R, and current spikes. That special frequency, f₀ = 1/(2π√(L·C)), is the circuit's natural note. A radio tunes a station by sliding f₀ onto it.

f0=12⋅π⋅L1⋅C1f_{0} = \frac{1}{2 \cdot \pi \cdot \sqrt{L_{1} \cdot C_{1}}} = 159.15 Hz resonant frequency — about 159 Hz here
✓ pass abs(2∗π∗f0∗L1−1/(2∗π∗f0∗C1))<0.001ohmabs(2 * \pi * f_{0} * L_{1} - 1 / (2 * \pi * f_{0} * C_{1})) < 0.001 ohm at f₀ the reactances really cancel
sqrt(100^2 + (2 * pi * x * 0.05 - 1 / (2 * pi * x * 20e-6))^2)
100150200100200300400

impedance vs frequency (Hz) — the dip at ≈159 Hz is resonance

Real-world hook: resonance is how a radio or TV picks one station from the air, how a metal detector and wireless charger work, and why a circuit can ring like a bell. Where next: AC Motors spins three of these waves into motion.