The time constant of a resistor–capacitor pair is τ = R · C, the time a capacitor takes to cover 63.2% of the gap to its target voltage. Drag the resistance, capacitance and supply voltage sliders below, then press Charge or Discharge and watch the curve, the current and the settling time respond.
Three sliders and three buttons drive everything on the panel. Resistance R spans 0.1 kΩ to 100 kΩ and Capacitance C spans 1 µF to 1000 µF; between them they fix every timing figure the lab prints. Supply voltage V0 runs from 1 V to 24 V and sets how tall the curve grows, nothing more. Charge sweeps the rising exponential from an empty capacitor, Discharge runs the falling one from a full capacitor, and Reset returns every slider to its opening position. One deliberate liberty: the sweep always takes about 2.4 seconds on screen whatever the physical τ happens to be, because a 100-second time constant animated honestly would look frozen. The canvas states that mapping under the time axis, and the axis itself is labelled in multiples of τ rather than in seconds.
Now drag the sliders and keep one eye on the τ readout. Double the resistance and it doubles; double the capacitance and it doubles again. Those are two different mechanisms with the same arithmetic result: resistance throttles how quickly charge is allowed to arrive, while capacitance decides how much charge has to arrive before the plates reach any given voltage. Then sweep the supply-voltage slider across its full range. The curve stretches upward, the peak-current figure climbs in exact proportion, and the τ readout does not shift by a single digit — a bigger supply pushes proportionally more current and demands proportionally more charge, and the two effects cancel.
Behind the graph the lab evaluates VC = V0(1 − e−t/τ) on a charge sweep and VC = V0 e−t/τ on a discharge, with I = (V0/R) e−t/τ in both directions. Slider units are converted before any of that runs — kilohms into ohms, microfarads into farads — which is exactly where a hand calculation usually slips by a factor of a thousand. If you need the arithmetic for your own component values rather than the picture, the RC time constant calculator handles the same formula and the same conversions.
The dashed cross-hair is the reason the lab exists. Its horizontal leg sits at 63.2% of the supply on a charge sweep, its vertical leg at one time constant, and the small gold ring marks where they meet on the curve. Read it once and the common shortcut — that a capacitor is “charged” after one τ — stops being tempting: at that moment more than a third of the gap is still open, and it takes five time constants to close 99.3% of it. Watch that ring while you move the voltage slider: it slides up and down the screen but never left or right, because timing belongs to R and C alone.
The resistance slider runs from 0.1 to 100 kilohms and the capacitance slider from 1 to 1000 microfarads; multiply them and you get the time constant, which drives every timing figure on the panel. The supply voltage slider, from 1 to 24 volts, sets the height the curve is heading for and the peak current at the instant the switch closes, but it has no say in how long the journey takes.
A larger supply pushes a proportionally larger current through the resistor, and it also demands a proportionally larger charge on the capacitor to reach any given fraction of the target. The two effects scale together and cancel exactly, so the shape of the curve in units of tau is identical at 1 volt and at 24 volts. Watch the tau readout while you drag the slider: it does not move a single digit.
Follow the dashed horizontal line at 63.2 percent of the supply voltage across until it meets the curve, then drop straight down to the time axis. That crossing point is one time constant, and the simulator marks it with a small gold ring so you can see it move as you change R and C. On a discharge sweep the same line sits at 36.8 percent instead, which is what is left rather than what has arrived.
Five time constants is the settling time, the point at which the capacitor has covered 99.3 percent of the gap to the supply voltage. The graph deliberately ends there because the remaining fraction is too small to see or to matter in most circuits. The panel prints the figure in milliseconds or seconds so you can compare it against a real timing requirement.
Yes. Press Discharge and the lab starts from a full capacitor and runs the falling exponential instead, with the guide line moved to 36.8 percent. The current readout behaves the same way in both directions because the current always decays from its peak, only its direction through the resistor reverses.