The Capacitor Charge-Discharge Time Constant Trick

Confused by how long it takes a capacitor to charge or discharge? There's a simple 'rule of 5' to estimate it!

Subject: electricity • Classes: 6–12 • Difficulty: intermediate (9-10)

The Trick

The time constant, $\tau = RC$, determines the charging/discharging rate. After $1\tau$, the capacitor charges/discharges to about 63%. It takes approximately $5\tau$ (five time constants) for a capacitor to be considered fully charged (99.3%) or discharged (0.7%). This 'rule of 5' avoids complex exponential calculations. The charging equation is $V(t) = V_0(1 - e^{-t/RC})$ and the discharging equation is $V(t) = V_0e^{-t/RC}$. After 5 time constants, $e^{-5} \approx 0.007$.

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