RC Charge Time
Time for a capacitor to reach a target percentage of the supply.
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The engineering
The exponential never quite arrives: 63% at 1τ, 95% at 3τ, 99% at 4.6τ, 99.9% at 6.9τ. Pick the settling target your measurement actually needs — waiting to 99.9% on every mux channel is how DAQ throughput dies.
Same math governs discharge; bleed-resistor sizing is this card run backwards.
Where this math comes from
This is the telegraph equation's simplest child — Kelvin's 1855 cable analysis again, where the exponential lag set how fast Victorian bankers could move money. The natural logarithm doing the work traces to Euler's formalization of e.
Every debounce circuit, every sample-and-hold spec, every 'wait 5τ' rule in a test procedure is this one line.
- 1748Leonhard Eulere and the exponential function formalized.
- 1855Lord KelvinRC transient law from telegraph cable theory.
See the full timeline of the math behind every calculator →
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