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:

Batteries store energy chemically. For a battery to create current, a chemical reaction must occur which converts chemical energy into electrical energy. Capacitors store electrical energy directly: hook a wire up to a capacitor and charge will immediately flow out of it. Capacitors are thus faster than batteries, and are already used in cases where you need a large amount of energy released quickly: camera flashes for example, or defibrillators. Batteries of equivalent size can't provide that much power. If your cellphone were powered by a capacitor instead of a battery, you could charge it fully in seconds.

The process of converting chemical energy to electrical energy in a battery is not 100% efficient; some energy is lost to heat. Because capacitors do not involve any energy conversion, they are more efficient than batteries.

Capacitors last much longer than batteries: they can be charged and uncharged millions of times without wearing out.

Capacitors usually use fewer toxic chemicals than batteries do.

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? :)