Capacitors & the RC Time Constant
A component that stores charge and, paired with a resistor, tells time. This lesson powers your final build's heartbeat.
Builds on: 0.1 Electric Charge & the Atom0.2 Voltage: Energy per Charge1.2 Ohm's Law
A bucket for charge
A capacitor is two conducting plates separated by an insulator. Push current in and charge piles onto one plate while the other is drained, building a voltage across the gap — Lesson 0.2’s charged plates, now as a component. How much charge it holds per volt is its capacitance:
One farad is enormous; real circuits use microfarads and smaller. Two habits to build now: electrolytic capacitors (the little cans, µF range) are polarized — the striped leg must go to the lower voltage or they can fail dramatically. And big charged capacitors keep their charge after power-off; treat them with respect.
Charging through a resistor: the exponential
Feed a capacitor through a resistor and it can’t fill instantly: the fuller it gets, the smaller the remaining voltage across R, the smaller the current refilling it. The result is the most famous curve in electronics — fast at first, ever slower, never quite arriving:
| elapsed | charged to |
|---|---|
| 1τ | 63% |
| 2τ | 86% |
| 3τ | 95% |
| 5τ | ≈ 99% — call it done |
The shape is universal. 1 kΩ × 100 µF gives τ = 0.1 s; 10 kΩ × 100 µF gives 1 s — same curve, different clock speed. Discharging mirrors it: down to 37% after one τ.
What capacitors are for
- Timing: charge to a threshold, trigger something, repeat — this is precisely how your 555 blinker will tick.
- Smoothing: a capacitor across a supply is a reservoir that fills the dips — every power supply has them.
- Blocking DC: once charged, no steady current flows through — but wiggles pass. Audio circuits couple stages this way.
- Energy storage: camera flashes dump a capacitor in a millisecond — power no small battery could deliver.
⚡ Lab — The Universal Curve
An RC circuit on a live oscilloscope. The time axis re-scales to whatever τ you dial in.
- Watch one full charge. Confirm it crosses the 63% line after one grid division (1τ).
- Flip to discharge mid-curve — the capacitor doesn’t care, it just heads for its new target.
- Change R and C wildly: the axis labels change, the shape never does.