Capacitors and Capacitance

A capacitor is a device purpose-built to store electric charge (and, along with it, electrical energy), consisting of nothing more than two conductors -- called its plates or electrodes -- placed close to one another and kept electrically insulated from each other, either by vacuum, by air, or by a dielectric medium filling the gap between them. When connected to a source of potential difference (such as a battery), one plate accumulates a charge $+Q$ and the other an equal and opposite charge $-Q$, with a corresponding potential difference $V$ established between them.

Definition of capacitance. For a GIVEN capacitor, experiment (and theory) shows that the charge $Q$ it holds is always directly proportional to the potential difference $V$ applied across it -- doubling $V$ exactly doubles $Q$, and so on. The constant of proportionality is called the capacitor's capacitance:

Capacitance is a property of the capacitor's own GEOMETRY (the size and shape of its plates, and the separation between them) and of the MEDIUM filling the gap between the plates -- it does not depend on the particular charge $Q$ or voltage $V$ used at any given moment, exactly as a container's volume does not depend on how much liquid happens to be poured into it at a given time. Different geometries and media give different capacitance values, but for one fixed capacitor, $C$ stays the same constant regardless of how it is charged.

SI unit. The unit of capacitance is the farad ($\text{F}$), defined so that $1\ \text{F} = 1\ \text{C/V}$: a capacitance of one farad means one coulomb of charge produces a potential difference of just one volt across the capacitor. A farad is, in practice, an enormous unit -- a capacitor storing a genuinely useful, everyday amount of charge for even a modest voltage typically has a capacitance measured in microfarads ($1\ \mu\text{F} = 10^{-6}\ \text{F}$), nanofarads ($1\ \text{nF} = 10^{-9}\ \text{F}$), or picofarads ($1\ \text{pF} = 10^{-12}\ \text{F}$), which is why these smaller submultiples, rather than the farad itself, are the units actually printed on most real capacitors. …