Capacitors and Capacitance

What is a Capacitor?

A capacitor is a system of two conductors separated by an insulator (dielectric). In the most common configuration, the two conductors carry equal and opposite charges: $+Q$ and $-Q$. The potential difference between them is $V = V_1 - V_2$.

• The charge of the capacitor is $Q$ (the magnitude of charge on one plate). The total charge of the system is zero.
• The conductors are charged by connecting them to the two terminals of a battery.

Why is Capacitance Defined?

The electric field $\mathbf{E}$ in the region between the conductors is directly proportional to the charge $Q$ on the plates. This follows from Coulomb’s law and the superposition principle: if $Q$ is doubled, $\mathbf{E}$ doubles at every point.

Since potential difference $V$ is the work done per unit positive charge to move a test charge from the negative to the positive plate against the field, $V$ is also proportional to $Q$.

Therefore, the ratio $\frac{Q}{V}$ is a constant for a given capacitor:

$C = \frac{Q}{V}$

This constant $C$ is called the capacitance of the capacitor.

What Does Capacitance Depend On?

• Geometrical factors: shape, size, and separation of the two conductors.
• Dielectric material: the nature of the insulator between the conductors (discussed later in the chapter). …