How a capacitor charges (and why it's never instant)

A capacitor stores charge. Connect it to a battery through a resistor and it fills up, but not at once. It starts fast and slows down as it gets full. That curve is behind every delay, timer and blinking light.

Pick values, then drag the time slider and watch the dot climb the curve.

Why it slows down

At the start the capacitor is empty, so the full battery voltage sits across the resistor. Lots of current flows and the capacitor fills fast.

As it charges, its own voltage goes up. Now there's less voltage left across the resistor, so less current flows, so it fills slower. It keeps getting closer to the battery voltage without ever quite reaching it.

The time constant

Everything about the curve comes from one number: resistance × capacitance, called the time constant (τ, the Greek letter tau).

10 kΩ × 100 µF = 1 second. Watch the units: 100 µF is 0.0001 F, and 10,000 × 0.0001 = 1.

• After 1 τ the capacitor is at 63% of the supply.
• After 2 τ about 86%.
• After 3 τ about 95%.
• After 5 τ about 99%. In practice that's "full".

So with 10 kΩ and 100 µF on 9 V: about 5.7 V after one second, practically 9 V after five. Double the resistor or the capacitor and everything takes twice as long.

Discharging is the same curve, upside down

Disconnect the battery and let the capacitor empty through a resistor. It drops fast first, then slower. After one time constant 37% is left, after five almost nothing.

The current does the same thing while charging: big at the start, then fading. That's why a lamp in series with a capacitor flashes bright and then fades out.

Where you use this

• Delays. A light that stays on a few seconds after you release a button.
• Timers and blinkers. The 555 timer charges and discharges a capacitor over and over. The resistors and capacitor set the speed.
• Smoothing. A capacitor across a power supply fills the gaps when the voltage dips.
• Button debouncing. A small RC filter hides the fast bouncing of a mechanical button.

Practical stuff

• Polarity. Electrolytic capacitors have a minus stripe. Put them in backwards and they can bulge, leak or pop. Ceramic ones don't care.
• Voltage rating. Pick a capacitor rated above your supply. For 9 V, a 16 V part is a good choice.
• Tolerance. Electrolytics are often ±20%. Your timing will be roughly right, not exact.
• Big capacitors bite. Even after you unplug, a large capacitor can stay charged. Discharge it through a resistor before you touch the leads.