A capacitor is a device that can store electric charge, and normally consists of two conducting objects (usually plates or sheets) placed near each other but not touching. Capacitors are widely used in electronic circuits. They store charge for later use, such as in a camera flash, and as energy backup in computers if the power fails. Capacitors also block surges of charge and energy to protect circuits.
Very tiny capacitors serve as memory for the “ones” and “zeros” of the binary code in the random access memory (RAM) of computers. Capacitors serve many other applications, some of which we will discuss.
A simple capacitor consists of a pair of parallel plates of area $A$ separated by a small distance $d$. Often the two plates are rolled into the form of a cylinder with plastic, paper, or other insulator separating the plates. In a diagram, the symbol represents a capacitor.
If a voltage is applied across a capacitor by connecting the capacitor to a battery with conducting wires, the two plates quickly become charged: one plate acquires a negative charge, the other an equal amount of positive charge.
Each battery terminal and the plate of the capacitor connected to it are at the same potential; hence the full battery voltage appears across the capacitor. For a given capacitor, it is found that the amount of charge $Q$ acquired by each plate is proportional to the magnitude of the potential difference $V$ between them:
$$ Q=CV $$
The constant of proportionality, $C$, in the above relation is called the capacitance of the capacitor. The unit of capacitance is coulombs per volt and this unit is called a farad ($F$).
Common capacitors have capacitance in the range of $1 \ pF$ (picofarad $= 10^{-12}F$) to $10^3\mu F$(picofarad $= 10^{-6}F$).
The capacitance $C$ does not in general depend on $Q$ or $V$. Its value depends only on the size, shape, and relative position of the two conductors, and also on the material that separates them.
For capacitors whose geometry is simple, we can determine $C$ analytically, and in this Section we assume the conductors are separated by a vacuum or air. First, we determine $C$ for a parallel-plate capacitor. Each plate has area $A$ and the two plates are separated by a distance $d$.
We assume $d$ is small compared to the dimensions of each plate so that the electric field $\vec{\mathbf{E}}$ is uniform between them and we can ignore fringing (lines of $\vec{\mathbf{E}}$ not straight) at the edges. The electric field between two closely spaced parallel plates has magnitude and direction is perpendicular to the plates. The field between the plates is
$$ E=\frac{Q}{\epsilon_0A} $$
The relation between electric field and electric potential, as given by
$$ C=\frac{Q}{V}=\epsilon\frac{A}{d} $$
Note that the value of $C$ does not depend on $Q$ or $V$, so $Q$ is predicted to be proportional to $V$as is found experimentally.