The RC Time Constant

A resistor and capacitor in series form the most important circuit in electronics. When a voltage is applied, the capacitor charges through the resistor along an exponential curve, and the time constant τ = R·C sets the pace: after one τ the voltage has reached 63.2% of the supply, and after five τ it is practically full.

Why the Exponential?

The charging current is proportional to the remaining voltage difference, so the closer the capacitor gets to full, the slower it charges — the hallmark of exponential approach. The same curve governs discharging, cooling, and every 'relaxation' process, from camera flashes to the decay of a capacitor's stored energy.

Time Constants and Filters

Viewed in the frequency domain, the same R·C product defines the cutoff frequency f_c = 1/(2πRC): the point where the circuit attenuates a signal to 70.7%. Below f_c a low-pass filter passes, above it blocks — the physics behind every audio tone control, anti-aliasing filter, and radio receiver.