EASA Part-66 · Module 3 — 3.7 Capacitance · B1/B2 Level 2

RC Charging, Discharging & the Time Constant

Objective: explain how the time constant τ = RC sets the speed of charge and discharge, and why a capacitor is ~fully charged after about 5 time constants regardless of the component values.

Circuit & current

Voltage across capacitor vs time

Supply voltage 12 V

Resistance R 10 kΩ

Capacitance C 100 µF

Playback speed 1.0 ×

Time t

0.00s

t in units of τ

0.00τ

0.00V

Current

0.00mA

Time constant τ

1.00s

5τ (≈ settled)

5.00s

% of final

0.0%

State

charging…

V_c = V(1 − e^−t/τ) · τ = R × C

The capacitor voltage rises (or falls) along an exponential curve. One time constant τ = RC is the time to cover 63.2% of the remaining gap; after about 5τ the change is over 99% complete. Bigger R or C means a longer τ — a slower curve — but the shape never changes.

Try this: Double R, then double C. What happens to τ, and to the time to reach the 5τ mark?
Try this: Set very different R and C values that give the same τ. Does the curve look any different?
Try this: Watch the current readout while charging. Why does the current fall as Vc rises?