Electromagnetism · Experiment

LC Oscillator

Charge a capacitor, connect it to an inductor, and the energy sloshes back and forth forever — electric field to magnetic field and back — the electromagnetic twin of a mass bouncing on a spring.

charge Q / energy in Ccurrent I / energy in Lcurrent flowdamping R (optional)

Controls

Frequency f₀ = 1/(2π√LC)—
Period T—
Energy in C: Q²/2C—
Energy in L: ½LI²—
Total energy—
Energy sloshes between the capacitor's electric field and the inductor's magnetic field — total stays exactly constant.
About this experiment ›

What you are looking at

A charged capacitor connected straight to an inductor. The capacitor drives a current through the coil; the coil's magnetic field then keeps that current flowing (inductors resist changes in current) until the capacitor is recharged the opposite way — and the whole cycle repeats. The animation is slowed to about one cycle every three seconds; the stats show the true frequency, which for these components is tens of hertz to kilohertz.

The oscillation equation

Kirchhoff's voltage law around the loop, with Q the capacitor charge and I = dQ/dt:
L·d²Q/dt² + Q/C = 0  ⇒  ω₀ = 1/√(LC)
This is exactly the simple-harmonic-motion equation. The charge swings as Q₀·cos(ω₀t), and the current — a quarter-cycle behind — as I₀·sin(ω₀t): when the plates are full the current is zero, and when the plates are empty the current peaks.

The spring analogy, made exact

Every quantity has a mechanical twin — the two systems share one mathematics:
L ↔ m  ·  1/C ↔ k  ·  Q ↔ x  ·  I ↔ v  ·  R ↔ friction
The inductor's reluctance to change current is inertia; the capacitor's push against more charge is the spring's stiffness. Energy alternates between Q²/2C (spring potential ½kx²) and ½LI² (kinetic ½mv²):
Q²/2C + ½LI² = constant
Watch the two energy bars — one drains exactly as the other fills, twice per cycle.

Adding resistance: the damped oscillator

Real circuits have resistance, which burns energy as heat exactly like friction. The swings then decay inside an exponential envelope, with the quality factor Q = (1/R)√(L/C) counting roughly how many cycles the oscillation survives. Set R to zero here for the ideal case — something a mechanical spring can never quite achieve.

Why it matters

An LC loop is nature's frequency-picker: it "rings" at exactly f₀ = 1/(2π√LC). Radio tuners, oscillator clocks, filters and wireless charging all start from this circuit — pick L and C, and you've picked a frequency.

Things to try

Quadruple L (or C) and watch the frequency halve — f₀ ∝ 1/√(LC). Raise Q₀ and the amplitude grows while the frequency stays put, just like a spring's period ignoring amplitude. Then add a few ohms and watch the decay envelope appear; compare with the damped spring simulator side by side.