electronics · 43 seconds
A tiny introduction to exponential curves.
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If resistance doubles, what happens to the time constant?
Illustrations generated with OpenArt. Narration uses free local Kokoro neural voices. Illustrations are visual aids; the written lesson carries the explanation.
Connect a capacitor to a constant-voltage source through a resistor. Its voltage rises quickly at first, then more slowly.
Fast first · slower later
Resistance times capacitance gives the time constant. 10000 ohms times 100 microfarads is one second.
τ = R × C = 1 s
After one time constant, an ideal charging capacitor reaches about 63 percent of its final voltage.
1τ → about 63%
After five time constants it reaches about 99.3 percent. The ideal exponential approaches its final value gradually.
5τ → about 99.3%
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