Capacitor Charge & Discharge Calculator NZ
This calculator works out the voltage on a capacitor at any moment as it charges or discharges through a resistor, the classic behaviour of an RC circuit. When a capacitor is connected to a supply through a resistor, it does not charge instantly: the voltage rises gradually along a curve, fast at first and then slowing as it approaches the supply voltage. Discharging mirrors this, falling quickly then tailing off toward zero. The pace is set by the time constant, the resistance times the capacitance, and after one time constant a charging capacitor reaches about 63 percent of the supply, after five it is essentially full. This exponential charging and discharging is the basis of timing circuits, filters, flashes, and the smoothing in power supplies. This tool computes the state at any instant. You enter the capacitance, the resistance, the supply voltage, the time elapsed, and whether the capacitor is charging or discharging, and the calculator returns the voltage at that time, the percentage charged or remaining, the charge stored at that moment, and the time constant. The results update as you type, so you can trace the curve by varying the time. Use it for electronics study, for designing timing and filter circuits, or to understand RC behaviour. Charging follows the supply voltage times one minus e to the minus time over the time constant; discharging follows the supply voltage times e to the minus time over the time constant. The time constant, resistance times capacitance, is the key scale: express your time as a multiple of it to read the curve easily, since the shape is always the same. Use scientific notation for the small capacitance values typical in real circuits.
Charging: V = supply x (1 - e^(-t/RC)). Discharging: V = supply x e^(-t/RC). Time constant = R x C. After 1 time constant a capacitor is ~63% charged. Mode below.
How it works
The time constant is the resistance times the capacitance. While charging, the voltage is the supply voltage times one minus e raised to minus the time divided by the time constant, rising toward the supply. While discharging, it is the supply voltage times e to that power, falling toward zero. The charge stored is the capacitance times the voltage at that time.
Worked example
With a 100 microfarad capacitor charging through a 1,000 ohm resistor from a 12 volt supply, the time constant is 0.1 seconds. After 0.1 seconds, exactly one time constant, the voltage is 12 times one minus e to the minus one, about 7.585 volts, or 63.2 percent of the supply, with a charge of about 758.6 microcoulombs.
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