When a voltage is applied to a capacitor through a resistor, the capacitor does not charge instantly. It takes time to build up charge. This delay is determined by the Time Constant (Tau, represented by τ).
Why is 1τ equal to 63.2%?
For a charging capacitor, V(t)=Vs·(1−e^(−t/RC)). At t=RC, V=Vs·(1−e^−1)≈0.632·Vs.
What does “5τ = fully charged” mean?
At 5τ, V≈Vs·(1−e^−5)≈99.3% of the final value. In most designs this is close enough to “fully charged”.
How do I compute time to reach a specific percentage?
Charging: t = −RC · ln(1 − V/Vs). Discharging: t = −RC · ln(V/V0).
Does capacitor tolerance affect delay time?
Yes. Real capacitors can be ±10% to ±20% (or more), so τ and timing will shift accordingly. Always check the datasheet tolerance.
Why is cutoff frequency shown here?
For a basic RC low-pass filter, the cutoff is fc = 1/(2πRC). This page shows it as a quick reference when τ is known.
What real-world effects are not included?
ESR, leakage, load resistance, and source impedance can change the curve—especially for large capacitors or high-speed signals.