Practical Uses of Capacitors

The first capacitors (called condensers at the time) were constructed in the 1700s, and their primary use was for storing charge for use in electrostatic experiments. Today, it is the energy-storing capabilities of capacitors which are of more interest. Capacitors offer certain advantages over batteries when it comes to storing energy:

This all sounds great, but there's one problem: capacitors can't store nearly as much energy as a battery of the same size.

Earlier we found that the capacitance of a sphere with radius \(0.5\u{m}\) is \(C=5.6\ten{-11}\u{F}\). If I charged this sphere up to \(110\u{V}\), and then pulled a \(1\u{mA}\) current off of it (which is something like the current required to power a cellphone), how long would that current run?
If I charge this sphere so that it is 110 V higher than \(V_{\infty}\), then the charge on the sphere will be $$Q=C\Dl V=(5.6\ten{-11}\u{F})(110\u{V})=6.2\ten{-9}\u{C}$$ A 1 mA current means that \(10^{-3}\u{C}\) of charge must leave the sphere every second. The the time it takes to completely empty the capacitor is $$t=\frac{6.2\ten{-9}\u{C}}{10^{-3}\u{C/s}}=6.2\u{\mu s}$$ What can you do with a cellphone in 6 microseconds? :)
As you can see in this example, our ability to replace batteries with capacitors is hampered by the very low values we've been finding for the capacitance. In the next section , we'll discuss how we can increase capacitance (besides the obvious step of making the capacitors really big).