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Capacitor charging

Transients · Intermediate · about 15 minutes · part of Zen’s Electronics Design Mastery

Through a resistor, a capacitor charges along an exponential curve. After one time constant τ = RC it reaches 63 % of the supply, and after 5τ it is practically full.

Capacitor charging: the circuit on the simulator's bench

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How it works

τ = R · C = 10 kΩ × 470 µF = 4.7 s

VC(t) = Vs + (V0 − Vs) · e−t/τ

1τ → 63.2 %, 2τ → 86.5 %, 3τ → 95.0 %, 5τ → 99.3 %

The scope’s 1 MΩ input also draws a little current, so the bench settles about 1 % low. Real instruments load circuits too.

Try it on the bench

  1. Hold the Discharge button to empty C, then click the toggle switch S and watch the curve on the scope.
  2. Read V_C after exactly one τ: about 63 % of 9 V, so roughly 5.7 V.
  3. Change R to 4.7 kΩ. The curve gets steeper.

Parts on the bench

In the course

Zen’s Electronics Design Mastery, module “Capacitors, Inductors & Time”.

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