Tau: the fundamental RC charging time
The time constant tau is the product of resistance (R) and capacitance (C), measured in seconds. When a capacitor charges through a resistor from an initial charge of zero, it reaches 63.2 percent of its final voltage in one tau. After five tau, it is 99.3 percent charged and is considered fully settled. This exponential charging follows e = 1 - exp(-t/tau), making tau the characteristic time for RC circuits. Smaller tau (lower R or C) means faster charging; larger tau means slower charging. This applies equally to RC discharge: a charged capacitor discharges to 37 percent of its starting voltage in one tau.
Practical timing and filtering applications
A camera flash circuit uses a large resistor and capacitor to charge slowly to high voltage (large tau for safety) and then discharge rapidly through the flash tube. An RC filter on a sensor output smooths noise: the input noise bandwidth is reduced by the cutoff frequency f_c = 1 / (2*pi*R*C), and the delay introduced is on the order of tau. Debouncing a switch uses tau to let mechanical bounce settle before registering a change. Understanding tau lets designers quickly estimate how fast an RC circuit responds without solving differential equations.