The RC time constant
Charge a capacitor through a resistor and the voltage doesn’t jump. It climbs along a curve that starts fast and levels off. The timescale of that curve is the time constant, τ = R × C. After one τ the capacitor has covered about 63% of the way to its final voltage. After five it’s effectively there. A 10 kΩ resistor and a 100 µF capacitor give τ = 1 second, slow enough to watch on a meter.
The shape follows from the parts’ own rules. Current through the resistor depends on how much voltage is still across it, so as the capacitor charges, the charging current shrinks and progress slows. Discharging runs the same curve in reverse. There’s no mystery in it, just Ohm’s law and capacitor behavior taking turns.
This one idea shows up all over real designs: power-on reset delays that hold a chip quiet until the supply settles, debounce filters that ignore switch chatter, simple timers, and every RC filter in the next lesson. When a datasheet asks for a 100 ms delay on a pin, an R and a C are usually how it’s done.
Key points
- τ = R × C sets the timescale of capacitor charge and discharge.
- One time constant covers about 63% of the change. Five is effectively complete.
- Charging slows as it goes, because less voltage remains to drive current.
- RC pairs build delays, debouncing, timers, and filters throughout real designs.
Practice
0 of 3 answered · Not startedWrong answers just let you try again, and hints are there if you want them. Answering every question first time, without hints, is what earns mastery.
- 1
After one time constant, a charging capacitor has reached what fraction of the applied voltage?
- 2
You need a longer delay from an RC network. What can you change?
- 3
What is the time constant of a 10 kΩ resistor with a 100 nF capacitor, in milliseconds?
ms
