RC time constant

When a resistor charges or discharges a capacitor, the voltage doesn't jump — it eases toward its final value along a smooth exponential curve, and the time constant τ = R·C sets how fast. Picture filling a bucket through a thin straw: at first water rushes in, but as the bucket fills the inflow slows, so the last bit takes ages. The product R·C, in seconds, is the natural pace of that approach.

After one time constant the capacitor voltage has covered about 63% of the gap to its final value; after about five time constants (5τ) it's within 1% and considered fully settled. This single number governs the speed of RC filters, the rise time of digital signals fighting wiring capacitance, the timing of 555-timer circuits, and the debounce delay of a button. Want a slower response? Increase R or C; want snappier? Shrink them.