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5.3.1. Capacitors

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A capacitor is a device that stores electric charge and electric energy. It is made from two conductors separated by an insulating region. The insulating region may be air, vacuum, glass, plastic, ceramic, or another nonconducting material. When one conductor has a positive charge and the other has an equal negative charge, an electric field forms between them, and energy is stored in that field.

Capacitors are very important in electricity and electronics because they can store charge temporarily and release it later. They are used in circuits for energy storage, filtering, timing, and many other purposes. In this chapter, the main goal is to understand what a capacitor is and how its basic property, capacitance, is defined.

Basic idea of a capacitor

Imagine two metal plates placed close to each other but not touching. If charge is moved from one plate to the other, one plate becomes positively charged and the other becomes negatively charged. Because opposite charges attract, the charges remain separated on the two plates. This separation of charge is the essence of a capacitor.

The two important physical quantities are the charge magnitude $Q$ on either conductor and the potential difference $V$ between them. The ratio of these quantities defines the capacitance.

The capacitance of a capacitor is defined by
$$
C = \frac{Q}{V}
$$
where $C$ is capacitance, $Q$ is the magnitude of the charge on either conductor, and $V$ is the potential difference between the conductors.

A larger capacitance means the capacitor can store more charge for the same voltage.

Meaning of capacitance

Capacitance tells us how easily a system of two conductors stores separated charge. It does not mean that the capacitor creates charge. Instead, charge is transferred from one conductor to the other, so the total charge of the pair remains zero if the capacitor is isolated.

If a capacitor has capacitance $C$, then

$$
Q = CV
$$

This equation shows that charge stored is proportional to voltage, for ordinary capacitors under normal conditions.

A capacitor with large capacitance needs less voltage to hold a given amount of charge. A capacitor with small capacitance needs more voltage to hold the same amount of charge.

Structure of a capacitor

Every capacitor has the same general structure:

  1. Two conducting parts.
  2. A separating insulating region.
  3. A potential difference between the conductors when charged.

The conductors are often called plates, even when their shape is not actually flat. In practice, capacitors can be built in many forms, such as flat plates, rolled foils, cylinders, or tiny layered structures inside electronic components.

The insulating material between the conductors prevents charge from simply flowing directly across. This allows charge to remain separated and energy to remain stored.

Basic capacitor structure

Charge on the plates

For an ideal capacitor, the two conductors carry equal and opposite charges. If one plate has charge $+Q$, the other has charge $-Q$. When we use the capacitance formula, $Q$ means the magnitude of the charge, not the algebraic sum.

For a capacitor,
$$
\text{charges on the two conductors are } +Q \text{ and } -Q
$$
and in the formula
$$
C = \frac{Q}{V}
$$
the quantity $Q$ is the magnitude of the charge on either conductor.

This is a common point of confusion. The net charge of the whole capacitor may be zero, but the capacitor still stores charge separation and energy.

Unit of capacitance

The SI unit of capacitance is the farad, abbreviated as $\mathrm{F}$.

From the definition,

$$
1 \, \mathrm{F} = 1 \, \frac{\mathrm{C}}{\mathrm{V}}
$$

where $\mathrm{C}$ means coulomb and $\mathrm{V}$ means volt.

One farad is a very large capacitance for many practical circuits, so smaller units are often used.

UnitSymbolValue
farad$\mathrm{F}$$1$
millifarad$\mathrm{mF}$$10^{-3}\,\mathrm{F}$
microfarad$\mu\mathrm{F}$$10^{-6}\,\mathrm{F}$
nanofarad$\mathrm{nF}$$10^{-9}\,\mathrm{F}$
picofarad$\mathrm{pF}$$10^{-12}\,\mathrm{F}$

How a capacitor is charged

A capacitor is usually charged by connecting it to a source of potential difference such as a battery. The battery does not place positive and negative charge out of nowhere. Instead, it moves electrons from one conductor to the other. One conductor loses electrons and becomes positively charged, while the other gains electrons and becomes negatively charged.

As charge builds up, the voltage across the capacitor increases. The charging process continues until the capacitor voltage matches the applied voltage, in an ideal simple setup.

Charging a capacitor with a battery

Dependence on geometry

Capacitance depends on the physical arrangement of the two conductors and the material between them. In general, capacitance becomes larger when the conductors can hold more separated charge for the same potential difference.

For example, for flat conductors facing each other, capacitance increases if the facing area is larger and decreases if the separation is larger. The detailed formula for a parallel plate capacitor belongs to the next chapter, but the qualitative idea is already useful here.

This means capacitance is determined by the shape, size, separation, and medium of the capacitor, not directly by the actual charge or voltage present at a given moment.

Capacitance is a property of the capacitor itself.
It depends on geometry and material, not on the instantaneous values of $Q$ and $V$, as long as the capacitor behaves linearly.

Energy stored in a capacitor

A charged capacitor stores energy because work must be done to separate charges. That energy is stored in the electric field between the conductors. The full discussion of energy stored in capacitors belongs to a later section, but it is important to know already that a capacitor is not only a charge storage device, it is also an energy storage device.

This is why capacitors can release electrical energy into circuits after being charged.

Symbol and ideal behavior

In circuit diagrams, a capacitor is represented by two nearby parallel lines. One line represents each conducting plate. In an ideal capacitor, no charge crosses the insulating region, and the relation $Q = CV$ is exact.

Common capacitor circuit symbol

Real capacitors are not perfectly ideal, but for basic physics this ideal model is the starting point.

Everyday intuition

A useful way to think about a capacitor is as a device that resists changes in voltage by temporarily storing separated charge. When connected in a circuit, it can charge up, hold energy, and later discharge.

You should not think of it as an empty container filled with charge. A better picture is that of two separated surfaces holding opposite charges, with an electric field between them.

Summary relationships

The key relations for a basic capacitor are simple and central.

Essential capacitor relations:
$$
C = \frac{Q}{V}
$$
$$
Q = CV
$$
SI unit:
$$
1\,\mathrm{F} = 1\,\frac{\mathrm{C}}{\mathrm{V}}
$$
A charged capacitor has equal and opposite charges on its two conductors:
$$
+Q \text{ and } -Q
$$

These ideas form the foundation for later study of specific capacitor types, combinations of capacitors, stored energy, and dielectrics.

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