Charging

In an RC circuit, the voltage of a capacitor changes as current flows in or out of it. This is evident because charge accumulates and creates a voltage in between the capacitor plates, so as more charge flows through, more voltage is created. Getting an equation for the voltage across a capacitor in an RC Circuit will require quite a bit of calculus.

Let's take this extremely simple circuit above and assume that the capacitor is initially discharged, that is, it has no charge. If the emf is being supplied throughout the circuit, we can use Kirchoff's Loop Rule to figure out expressions for the voltages at both the resistor and capacitor.

Now, we want to find the expression for the voltage through a capacitor while it discharges.

In these boxed expressions, t is the time elapsed and RC is the time-constant. This time constant is simply the product of the total resistance, R, and the capacitance of the capacitor, C. This makes sense because if either the resistance or capacitance is greater, the time it takes to charge or discharge the same voltage will be much longer.