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τ = RC: the smallest useful equation in electronics.
One resistor and one capacitor set a time scale: τ = RC. That single number defines how fast a capacitor charges (63.2% in one τ), where a filter starts cutting (f = 1/2πRC), and how long a switch bounce lasts. This calculator converts your R and C into the time constant, cutoff frequency, and charge-time benchmarks.
Electronics hobbyists use it for debounce and filter design; EE students live in it during circuits courses. The 1τ/63.2% benchmark is the fastest way to read a scope trace without a cursor.
At f = 1/(2πRC), a low-pass RC filter passes half power (−3 dB) — the signal drops to 70.7% amplitude. Above cutoff the signal rolls off at 20 dB per decade; below it, the signal passes nearly untouched. Put the cutoff at least a decade away from frequencies you must preserve or reject for clean behavior.
Never completely — it is asymptotic. 1τ gets 63.2%, 3τ gets 95%, 4.6τ gets 99%, 5τ gets 99.3%. Digital designs usually wait 5τ before assuming a settled voltage; analog designs check the ripple spec against the actual exponential.
Switch debouncing (τ of a few ms kills bounce), power supply smoothing, 555 timer periods, audio crossovers, ADC input settling, and reset circuits. It is also the reason long wires and high impedance don't mix: stray capacitance forms an accidental RC filter with your source resistance.