Chargetta

Meet Chargetta, a capacitor who fills up fast at first and then takes her time.

When a capacitor is connected to a battery through a resistor, charge flows onto its plates. At first the capacitor is empty, the full supply voltage drives current through the resistor, and charging is quick. As charge builds, the capacitor's own voltage pushes back, the current shrinks, and charging slows. The result is the exponential curve V(t) = V₀(1 − e^(−t/RC)), set by the time constant RC.

After one time constant the voltage reaches 1 − e⁻¹ ≈ 63.2 percent of the supply. With R = 10 kΩ and C = 100 µF, RC = 10,000 × 0.0001 = 1 s. After five time constants, 5 s, it reaches 1 − e⁻⁵ ≈ 99.3 percent.

RC circuits set delays and timing in electronics, smooth power supplies, and charge camera flash units.

Strictly, the capacitor never reaches 100 percent; engineers call it full after about five time constants. Real capacitors also leak slowly, and the formula assumes an ideal resistor and constant supply.