A capacitor will not hold its charge forever. This is because the air around it conducts very slightly. So a small current flows from the positive plate to the negative plate, discharging the capacitor. But how long will this take and can we speed it up?
A simple discharge circuit
Picture 5.10 shows a circuit with a charged capacitor and a 40 W resistor. When the switch is closed, the capacitor will discharge through the resistor. Let's see what happens to the current in the circuit. We will follow the discharge in small steps of time and build up the values in table 1. (Roll your cursor over the steps to build up the table and the graph.)
We can always recognise an exponential curve because the y-axis changes by an equal proportion for equal divisions on the x-axis. For example, bacterial growth is often exponential it doubles every 3 seconds. Radioactive decay is exponential the activity of carbon-14, for example, halves every 5700 years. Now we can see that our capacitordischarging through a resistor is exponential it drops to 87.5% of its starting value every 10 ms.
Does it reach zero?
Although, in theory, exponential curves never reach the origin, in reality a capacitor will always discharge. Here are two views as to why:
The engineer: it will eventually get so small that we cant measure it.
The physicist: it will eventually get down to a small number of individual electrons on the negative plate. These will, randomly, leave the plate.
Even so, we cant measure the time it takes to fully discharge. So we have to measure how long it takes to reach a certain proportion (rather like half lives for radioactive isotopes). Well see how on the next page.