Inside the capacitor
Two conductors with an insulator between them: the simplest part in electronics, and in every circuit you own. Every picture below is computed while you watch, from the same equations as the textbook. Move the sliders.
What it is
A capacitor stores energy in an electric field. Connect it to a voltage and electrons are pushed onto one plate and pulled off the other. No charge crosses the insulator (the dielectric); the plates simply end up holding equal and opposite charges, and the field between them holds the energy.
C = ε₀ · εr · A / d Q = C · V U = ½ · C · V²
The capacitance C, in farads, grows with plate area A and with the dielectric’s relative permittivity εr, and shrinks as the gap d widens; ε₀ = 8.854 × 10⁻¹² F/m. Every kind of capacitor is a different answer to one problem: huge area, tiny gap and high εr, without the dielectric breaking down.
How it’s made
How it works: charging and discharging
A battery, a resistor and two plates. The current is i = (Vbattery − v) / R: large at first, then smaller as the plates’ own voltage v builds up and pushes back. That gives the curve every electronics student learns, v = V(1 − e^(−t/RC)), and the time constant τ = R·C.
Not to scale: electrons really drift millimetres per second (the signal moves at nearly the speed of light); here their speed shows the current. The time is stretched or squeezed so one τ takes 2.5 s on screen. The electrolytic preset breaks down near 16 V because its oxide is 22 nm thick, which is why it is rated 16 V. An MLCC is hundreds of thin layers; the preset adds their area up.
What to notice
- The current is largest at the start, when the capacitor is empty, and falls as it fills: an empty capacitor behaves like a short circuit, a full one like an open circuit.
- After one τ the capacitor is at 63 %; after five, it is effectively full. A bigger R or a bigger C makes it slower.
- Halve the gap and C doubles, but so does the field: the voltage it can take falls. That trade-off is why rated voltage and capacitance fight each other in every real capacitor.
- With X7R ceramic and a thin gap, εr drops as the voltage rises: a class-2 MLCC gives much less than its marked value at DC bias.
The dielectric up close
The molecules of a dielectric are tiny dipoles, or become dipoles in a field. The plates’ field turns them; heat jostles them back. Lined up, they leave a layer of bound charge at each surface that cancels part of the plates’ field, so the field inside is only E₀ / εr. Less field for the same charge means less voltage, so the same voltage stores εr times more charge.
Each arrow is a dipole: red end +, blue end −. Raise the temperature and they jiggle out of line; that is one reason εr changes with temperature.
With AC: reactance and the 90° lead
With a sine wave the capacitor never finishes charging. The current is i = C · dv/dt: biggest when the voltage is changing fastest (crossing zero), a quarter cycle before the voltage peaks. Its opposition to AC is the reactance Xc = 1 / (2π f C): high at low frequency, low at high frequency. That is how capacitors block DC, pass AC, and filter.
10 V peak. The plot always shows two cycles; the readings carry the real frequency and current.
What goes wrong
Capacitors fail in a few classic ways, and the aluminium electrolytic, the one in every power supply, shows them all. Its dielectric is an oxide only nanometres thick, grown on the positive foil. Reverse it, or push it past its surge voltage, and current leaks through the oxide; the electrolyte breaks down into gas, the can heats and bulges, and the scored vent on top opens. Even within its ratings, heat is what ends it: ripple current heats its internal resistance (ESR), the electrolyte slowly dries out, and life halves for every 10 °C hotter.
A 470 µF 16 V 105 °C part, ESR 0.15 Ω. The leakage and heating curves are typical shapes, not one maker’s datasheet.
- Dielectric breakdown: past the dielectric strength an arc punches through. Film capacitors self-heal (the thin metal burns away around the fault); ceramics and electrolytics usually short.
- MLCC cracks: a ceramic chip bent on its board (a flexing PCB, a hot iron) cracks inside and can short later.
- DC bias and ageing: class-2 ceramics lose capacitance with voltage and, slowly, with time.
- Dry-out: the bulging-top capacitors in old power supplies and monitors are electrolytics that ran hot for years.
Use it on the bench
Every lesson below opens in the lab with a real circuit: change the parts and measure with the meter and the scope, the same physics as above, now in a circuit.
- Capacitor charging — watch v rise along 1 − e^(−t/RC) on the scope (about it)
- Capacitor discharging — the same curve on the way down (about it)
- Capacitors in series and parallel — parallel adds, series divides (about it)
- RC low-pass filter — a capacitor and a resistor as a filter (about it)
- Bridge rectifier and filter — the big electrolytic that smooths a power supply, and its ripple (about it)
- Capacitor ESR check — measure ESR, the number that ages a capacitor (about it)
Check yourself
Exam-style questions (ECE, EE and NC-II reviewers ask these). Each answer links to the scene that shows it.
1. A parallel-plate capacitor has its plate gap halved and nothing else changes. Its capacitance:
C = ε₀·εr·A/d: capacitance is inversely proportional to the gap. Try it with the gap slider in the first scene. See the scene ▸
2. A 100 µF capacitor charges through 10 kΩ from 12 V. After one time constant it is at about:
τ = RC = 1 s, and after one τ the voltage is 1 − e⁻¹ ≈ 63.2 % of the supply: 0.632 × 12 ≈ 7.6 V. After 5 τ it is within 1 %. See the scene ▸
3. The energy stored in a 2 200 µF capacitor at 25 V is about:
U = ½·C·V² = 0.5 × 0.0022 × 625 ≈ 0.69 J. Doubling the voltage stores four times the energy. See the scene ▸
4. What does a dielectric do between the plates?
The aligned dipoles leave bound charge at the surfaces that cancels part of the plates’ field; the field inside falls to E₀/εr, so for the same voltage the plates hold εr times more charge. See the scene ▸
5. A 1 µF capacitor at 50 Hz has a reactance of about:
Xc = 1/(2πfC) = 1/(2π × 50 × 10⁻⁶) ≈ 3 183 Ω. At 5 kHz it would be 100 times less. See the scene ▸
6. In a capacitor fed with a sine wave, the current:
i = C·dv/dt: the current is greatest where the voltage is changing fastest (crossing zero), a quarter cycle before the voltage peaks. See the scene ▸
7. A 10 µF X7R ceramic capacitor rated 16 V is run at 12 V DC. Its capacitance is most likely:
Class-2 ceramics (barium titanate) lose permittivity under DC bias: at a good fraction of the rated voltage a 10 µF part may give 3–5 µF. Try X7R with a thin gap in the first scene and watch εr fall. See the scene ▸
8. Why does an aluminium electrolytic have a polarity?
The oxide only holds off voltage one way. Reversed, it is reduced, leakage rises steeply, the electrolyte gasses and heats, and the vent opens. See the last scene. See the scene ▸
9. An electrolytic rated 2 000 h at 105 °C runs at 65 °C. A rough life estimate is:
The rule of thumb: life doubles for every 10 °C cooler. 40 °C cooler is 2⁴ = 16 times: 32 000 h, a little under four years of continuous running. See the scene ▸
10. The usual way an MLCC holds microfarads in a 1 mm chip is:
Stacking hundreds of printed electrodes adds the layers in parallel, and barium titanate has εr in the thousands. See “How it’s made”, MLCC, step 3. See the scene ▸
Inside the other parts
The inductor (the capacitor’s magnetic twin) · the transformer · the resistor · the diode and LED · the transistor · the battery · all the parts