Constante de tempo RC

RC time constant: τ = R · C

The RC time constant τ = R · C tells you how quickly a capacitor charges or discharges through a resistor. Charging follows V(t) = Vf · (1 − e−t/τ). After 1τ the capacitor sits at 63 % of the final voltage, and by 5τ it's at 99.3 %, which is the point everyone treats as fully charged. As an example, R = 10 kΩ with C = 100 µF gives τ = 1 s, so a full charge takes roughly 5 s. That same RC pair also sets the cutoff of a first-order low-pass filter: fc = 1 / (2π · R · C).

Applications: debounce, filters, switching supplies

You'll see RC pairs doing switch debounce, where a τ around 10–50 ms smooths out mechanical bounce, plus audio filters, ripple smoothing in switching supplies, and antialiasing in front of an ADC. A smaller τ gives a faster response and pushes the cutoff frequency up.

FAQ

Why 63 % at one time constant? It falls right out of the exponential solution to the charging equation, since 1 − e⁻¹ ≈ 0.632.

When is the capacitor "fully" charged? Strictly speaking, never. By 5τ it's within 0.7 % of the target, and that's close enough that we call it full in practice.

How do I pick R and C for a 100 Hz cutoff? Start by choosing C, say 100 nF, then solve R = 1 / (2π · f_c · C) ≈ 15.9 kΩ.