How a capacitor charges through a resistor

When the switch closes, current rushes into the empty capacitor, but the resistor limits how fast. As charge builds up, the capacitor pushes back with its own voltage, so the current shrinks and charging slows. The product of resistance and capacitance, the time constant, tells you how long it takes to reach about 63 percent of full charge.

Controls

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Animation speed

Resistance

Capacitance

Time after closing the switch

Step through it

Closing the switchAt time zero the capacitor is empty, so the full 9 volts sits across the resistor and the current is at its largest.
The resistor sets the paceCurrent through the resistor equals the voltage across it divided by its resistance. A bigger resistor means a smaller trickle of charge.
The capacitor pushes backCharge collects on the capacitor plates, raising its voltage. That leaves less voltage across the resistor, so the current keeps shrinking.
One time constantAfter one time constant, R times C, the capacitor reaches about 63 percent of the supply voltage.
Five time constantsAfter about five time constants it is over 99 percent full and the current has nearly stopped.

The charging curve

For a capacitor charging from a constant supply V through a resistor R, the capacitor voltage is Vc = V x (1 minus e^(minus t / RC)) and the current is I = (V / R) x e^(minus t / RC). The time constant tau = R x C comes out in seconds when R is in ohms and C is in farads.

Kilohms times microfarads gives milliseconds, so 10 kilohms and 100 microfarads gives 1,000 milliseconds, or one second. The model assumes an ideal 9 volt battery and a perfect capacitor with no leakage.

Try it: leave the time at 1 second and change the capacitor from 100 to 1000 microfarads. The time constant grows tenfold and the capacitor voltage drops from 5.7 volts to under 1 volt.

Where RC timing shows up

RC pairs set the delay in timers, smooth the ripple out of power supplies, debounce buttons and filter noise from sensor signals. The same math describes many sensors that respond gradually rather than instantly.

Sources

Charging a CapacitorHyperPhysics, Georgia State University
RC Circuits (Physics 114 lecture)University of Rochester
DOE Fundamentals Handbook: Electrical Science, Volume 2 (capacitive time constant)U.S. DOE Office of Scientific and Technical Information

How to cite this model

Avid Solutions International. (2026, November 11). How a capacitor charges through a resistor [Interactive 3D model]. Avid Field Lab. https://avidsolutionsintl.com/explore/rc-circuit

Last updated November 11, 2026

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