How it works
The time constant τ (tau) is the resistance multiplied by the capacitance. After one τ a charging capacitor reaches about 63.2% of the supply voltage; after five τ it is above 99% and is usually treated as fully charged.
The same R and C used as a low-pass filter pass frequencies below the cutoff and attenuate those above it, by 3 dB at exactly the cutoff frequency.
τ = R × C
V(t) = Vs × (1 − e^(−t/τ))
fc = 1 / (2π × R × C)Worked example
10 kΩ with 100 µF gives τ = 10,000 × 0.0001 = 1 s. The capacitor reaches 63% in 1 s and over 99% in 5 s. As a filter, the cutoff is 1 / (2π × 1) ≈ 0.159 Hz.