LC Resonance
A capacitor and an inductor trade energy back and forth like a pendulum — every circuit's natural note.
Builds on: 2.3 Capacitors & the RC Time Constant2.4 Inductors & Electromagnetism5.3 Impedance & RC Filters
The electrical pendulum
You know both players. A capacitor stores energy in its electric field (2.3); an inductor stores it in a magnetic field (2.4). Connect them in a loop — a tank circuit — charge the capacitor, and let go. The capacitor pushes current through the coil; the coil’s field builds; when the capacitor is empty the coil refuses to stop (inductors hate change!) and keeps pushing, charging the capacitor the other way. Then the whole dance reverses. Voltage and current swap leadership 90° apart, exactly like a pendulum trading height for speed.
This isn’t a metaphor — it is mathematically the same equation as a mass on a spring. Physicists call every such system a harmonic oscillator; you have just built the electrical one.
Q: how pure is the bell?
Real loops have resistance, and every slosh loses a little energy to heat — so the ring decays. The Q factor counts roughly how many times the tank rings before dying (more precisely, Q ≈ √(L/C)/R for a series loop). A high-Q tank is a tuning fork: struck once, it hums for ages, and — the flip side that matters for radio — it responds enthusiastically only to frequencies very near f₀. A low-Q tank is a struck pillow.
Resonance is everywhere
- Radio tuning — next lesson, and the reason this unit exists.
- Crystals: quartz resonators are mechanical LC-equivalents with Q in the tens of thousands — they discipline every clock you own (remember the 32 768 Hz watch crystal from 7.3?).
- Wireless charging: two coils resonating at the same frequency pass power across an air gap.
- The dark side: unintended resonances make bridges gallop and audio circuits howl. Engineers spend careers adding damping.
Your RC filters (5.3) could only slope gently up or down. An LC pair gives filters a peak — a band-pass that favours one frequency. That peak is the whole secret of the next lesson.
⚡ Lab — Ring the Bell
A tank circuit you can kick, with the energy see-saw made visible.
- Kick it and watch voltage (cyan) and current (amber) chase each other, 90° apart.
- Quadruple C (100 nF → 400 nF): the note drops exactly one octave (f₀ ∝ 1/√C).
- Raise the loop resistance: same note, but the bell dies young. That’s Q.