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Capacitor — the exponential clock (RC time constant)

electronics

A capacitor charging through a resistor follows V(t) = V·(1 − e^(−t/RC)); after one time constant τ = RC it holds exactly 1 − 1/e ≈ 63.2% of the supply — sealed in-domain (1000 Ω × 1000 µF = 1 s; 5 V → 3.1606 V at t = 1 s): https://narrowhighway.com/s/1ee0d3ed486453eee0967146a531984888709198b39fb16a7b2c2a5f58ef1b73 . Every timer, filter, and debounce circuit is this one exponential wearing different values. Real parts add leakage and ESR — empirical, not sealed.

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