RC time constant formula
The RC time constant sets how fast a capacitor charges or discharges through a resistor. It is simply the resistance times the capacitance, and it governs timing, filtering, and smoothing in electronic circuits.
What each symbol means
| Symbol | Meaning | Units |
|---|---|---|
| τ | Time constant | seconds (s) |
| R | Resistance | ohms (Ω) |
| C | Capacitance | farads (F) |
Rearranged forms
Worked example
A 10 kΩ resistor charges a 100 µF capacitor. Find the time constant.
- Start from τ = R C.
- Convert units: R = 10,000 Ω, C = 0.0001 F.
- Multiply: τ = 10000 × 0.0001.
Work in ohms and farads to get seconds. Capacitors are usually marked in microfarads (µF) or nanofarads, so convert first. After one time constant the capacitor reaches about 63% of the supply; after five it is essentially fully charged.
Designing a timing or filter circuit?
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How the time constant works
When a capacitor charges through a resistor, the current tapers off as the capacitor fills. The time constant is the time to reach about 63% of the final voltage. Larger resistance or capacitance slows the process; smaller values speed it up. Full charge is reached in roughly five time constants.
Where it is used
RC time constants set delays in timers, the cutoff of simple filters, debounce timing for switches, and the smoothing of power supplies. The same R and C values also set a low-pass filter's cutoff frequency.
FAQ
What is the RC time constant?
τ = R C, the resistance times the capacitance, in seconds. It sets how quickly a capacitor charges or discharges.
How long until the capacitor is fully charged?
About five time constants. After one it reaches 63%, after three about 95%, and after five over 99%.
What units do I use?
Ohms and farads give seconds. Since capacitors are often in microfarads, convert to farads first (1 µF = 0.000001 F).