What is a capacitor?

What is a capacitor made of?

Every capacitor has the same basic design: two conducting plates with an insulator, called the dielectric, between them. The plates may be metal foils rolled up into a tube, thin layers stacked in a tiny ceramic chip, or, in the simplest case, two flat sheets facing each other. No current can flow through the insulator, which is the key to how a capacitor behaves.

What does a capacitor do?

Connect a capacitor to a battery and electrons flow onto one plate and off the other. One plate becomes negatively charged and the other equally positive. Current flows in the wires while this happens, even though no charge crosses the gap. As charge builds up, the voltage across the capacitor rises until it matches the battery, and then the current stops. The capacitor is now charged.

Disconnect the battery and the charge stays put. Connect the capacitor across a lamp or resistor, and the charge flows back round the circuit, discharging it. Unlike a battery, which makes energy from a chemical reaction slowly, a capacitor can only store what you put in, but it can give it all back very quickly.

Capacitance: Q = CV

Capacitance (C) is how much charge a capacitor stores for each volt across it. OpenStax University Physics defines it as charge per volt:

The unit is the farad (F): one farad stores one coulomb per volt. That is a lot, so most capacitors are measured in microfarads (μF, millionths of a farad), nanofarads (nF) or picofarads (pF, millionths of a microfarad).

Example: a 680 μF capacitor with 9 V across it holds Q = 680 × 10⁻⁶ × 9 = 0.00612 C, which is 6.12 mC.

Why one farad is so big

For two flat plates with air or a vacuum between them, C = ε₀A ÷ d, where A is the plate area, d is the gap and ε₀ = 8.85 × 10⁻¹² F/m. Two plates 10 cm square (0.01 m²) and 1 mm apart give C = 8.85 × 10⁻¹² × 0.01 ÷ 0.001 = 8.85 × 10⁻¹¹ F, just 88.5 pF. To reach 1 F with a 1 mm gap, the plates would need an area of about 113 km². Real capacitors get big values with huge rolled up areas, tiny gaps and dielectrics that boost the capacitance.

Energy stored in a capacitor

The ½ is there because the voltage rises gradually from zero as the capacitor charges, so on average each coulomb was pushed on at half the final voltage. The 680 μF capacitor at 9 V stores E = ½ × 680 × 10⁻⁶ × 9² = 0.0275 J, about 28 mJ. That is small, but it can be released in a fraction of a second, which is what a camera flash needs.

Charging and discharging: the time constant

When a capacitor charges through a resistor, it doesn't fill at a steady rate. It charges quickly at first, then more and more slowly, because the rising voltage across it leaves less voltage to push current through the resistor. How fast this happens is set by the time constant:

After one time constant, a charging capacitor reaches about 63.2% of its full charge, and a discharging one is left with about 36.8%, according to OpenStax. After about 5 time constants it is effectively full or empty. The charging voltage is V = V₀(1 − e^−t/RC), and the discharging voltage is V = V₀e^−t/RC.

Worked example: charging through a resistor

A 100 μF capacitor charges from a 9 V battery through a 10 kΩ resistor. The time constant is τ = 10,000 × 0.0001 = 1 s.

Here x is the time in seconds and y is the voltage across the capacitor in volts. It rises steeply, then levels off towards 9 V. Halving the resistor or the capacitor would halve the time constant and make the curve twice as steep. You can run this circuit in the RC timing mode of our Circuit Builder.

Try one: this question gives you a resistor and a capacitor and asks for the time constant.

Capacitors in series and parallel

The rules are the opposite way round from resistors. In parallel, capacitances add, because it is like making the plates bigger: 220 μF and 330 μF in parallel make 550 μF. In series, the reciprocals add, so the total is smaller than either: 1 ÷ (1/220 + 1/330) = 132 μF.

What are capacitors used for?

• Smoothing power supplies. A capacitor charges on each peak of a rectified AC supply and tops up the output in between, turning a bumpy voltage into a steadier one.
• Timing. The time constant sets how long a circuit waits, from flashing lights to the delay before a car's interior light fades.
• Filtering and decoupling. Capacitors pass changing signals but block steady DC, so they remove noise or separate an audio signal from a DC voltage. Small ones sit next to chips to steady their supply.
• Short bursts of power. A camera flash charges a capacitor slowly from a battery, then dumps the energy into the flash tube at once.
• Touchscreens. Your finger changes the capacitance of a grid of electrodes under the glass, which the phone detects.
• Computer memory. Each bit in DRAM is stored as a tiny charge on a microscopic capacitor.

How to test a capacitor

How to test a capacitor with a multimeter

1. Remove it from the circuit if you can, so other parts don't affect the reading, and make sure it is discharged.
2. Check the markings. Note the capacitance and voltage rating. For an electrolytic capacitor, note which lead is negative, usually marked with a stripe.
3. Use the capacitance setting (often marked with the capacitor symbol) if your meter has one. Connect the probes, positive to positive for an electrolytic, and wait for the reading to settle.
4. Compare the reading with the label. It should be within the tolerance printed on the capacitor. A reading far too low suggests it has dried out or failed; zero or "OL" can mean it is open or shorted.
5. No capacitance mode? On a resistance setting, a healthy capacitor shows a resistance that starts low and climbs as the meter's small current charges it. A reading stuck near zero means it is shorted.

That climbing reading is the charging curve above in action: the meter is the battery, and the reading rises as the capacitor fills.

Common mistakes

• Thinking current flows through a capacitor. Charge flows onto and off the plates; none crosses the insulator.
• Forgetting to convert μF to F. 100 μF is 100 × 10⁻⁶ F = 0.0001 F.
• Using the resistor rules for capacitors. Capacitors add in parallel, not series.
• Leaving out the ½ in the energy formula. E = ½CV², not CV².
• Thinking a capacitor is fully charged after one time constant. It is only about 63% charged; allow about 5 time constants.
• Connecting an electrolytic capacitor backwards. These are polarised and can fail, sometimes violently, if reversed or over their voltage rating.

Read next

Physics · Electricity and magnetismSeries and parallel circuits: rules, resistors, examplesSeries and parallel circuits explained: current, potential difference and resistance rules, resistors in parallel, and worked GCSE and A-level examples.