How a capacitor charges

A capacitor stores electric charge. When it is connected to a battery through a resistor, it doesn't fill up instantly. It charges quickly at first and more and more slowly as it fills. That simple behaviour is behind delays, timers and blinking lights, including the 555 timer later in the course. You only need Ohm's law to follow this page.

What a capacitor is

A capacitor is made of two conducting plates separated by a thin insulating layer. Current can't flow through the insulator, but when a voltage is applied, charge collects on the plates, positive on one side and negative on the other. The amount of charge it can hold for each volt is its capacitance, measured in farads (F).

One farad is a very large amount, so real capacitors are given in microfarads (µF, millionths of a farad), nanofarads (nF, thousandths of a microfarad) and picofarads (pF). A 100 µF capacitor is 0.0001 F.

There are two common kinds. Electrolytic capacitors hold large values, from about 1 µF upwards, and have a plus and a minus leg. The minus side is marked with a stripe on the body. Ceramic capacitors are small, hold smaller values, and can be connected either way round.

Why it slows down

At the moment you connect the battery, the capacitor is empty and has no voltage across it, so the full battery voltage sits across the resistor and a large current flows. As charge builds up, the capacitor's voltage rises. That leaves less voltage across the resistor, so the current gets smaller and the charging slows down. The capacitor's voltage keeps getting closer to the battery voltage without ever quite reaching it.

The time constant

How fast this happens depends on the resistance multiplied by the capacitance. That product is called the time constant, written with the Greek letter τ (tau), and it comes out directly in seconds when you use ohms and farads. With 10 kΩ and 100 µF: 10,000 × 0.0001 = 1 second.

• After 1 τ the capacitor is at about 63% of the supply voltage.
• After 2 τ, about 86%.
• After 3 τ, about 95%.
• After 5 τ, about 99%, which in practice counts as full.

So with 10 kΩ, 100 µF and 9 V, the capacitor reaches about 5.7 V after one second and is practically full after five. Doubling either the resistor or the capacitor makes everything take twice as long.

Discharging follows the same curve in reverse. If the charged capacitor is connected to a resistor on its own, its voltage falls quickly at first and then more slowly. After one time constant about 37% is left.

The current behaves the same way. It is largest at the start and then fades, which is why a lamp in series with a capacitor lights up brightly for a moment and then goes dark.

Where this is used

• Delays, such as a light that stays on for a few seconds after a button is released.
• Timers and oscillators, which charge and discharge a capacitor over and over. The 555 timer works this way.
• Smoothing, where a capacitor across a power supply fills in short dips in the voltage.
• Debouncing, where a small resistor and capacitor hide the rapid on-off flickering a mechanical button produces when pressed.

Practical points

• Connect electrolytic capacitors the right way round. Reversed, they can bulge, leak or burst.
• Choose a capacitor whose voltage rating is above your supply. For a 9 V circuit, a 16 V rating is a good choice.
• Electrolytic capacitors often have a tolerance of ±20%, so timings based on them are approximate.
• Large capacitors can stay charged after the power is removed. Discharge them through a resistor before touching their legs.