← Concept Lab

The RC Charging Curve

A capacitor charging through a resistor from a constant source Vs follows V(t) = Vs * (1 - e^(-t/RC)). The time constant tau = R*C sets how fast: at t = tau the capacitor has reached about 63.2% of Vs. Drag R and C and watch the curve approach Vs faster or slower. Here R is in kilo-ohms and C in milli-farads, so tau = R*C is in seconds.

Time constant tau = R*C (s)
1.000
V at t = tau (~63.2% of Vs)
3.160

Bigger R or bigger C means a longer time constant and a slower charge, but the voltage always approaches Vs and never overshoots it. The dashed marks show t = tau and 0.632*Vs. This is a fixed demonstration concept (NOVA's interactive-visual modality); the per-misconception, per-course generated version is the frontier work that follows.