Capacitors and Dielectrics

Capacitors and Dielectrics

A capacitor is a device used to store electric charge. Capacitors have applications ranging from filtering static out of radio reception to energy storage in heart defibrillators. Typically, commercial capacitors have two conducting parts close to one another, but not touching, such as those in this figure. (Most of the time an insulator is used between the two plates to provide separation—see the discussion on dielectrics below.) When battery terminals are connected to an initially uncharged capacitor, equal amounts of positive and negative charge, \(+Q\) and \(–Q\), are separated into its two plates. The capacitor remains neutral overall, but we refer to it as storing a charge \(Q\) in this circumstance.

The amount of charge \(Q\) a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.

A system composed of two identical, parallel conducting plates separated by a distance, as in this figure, is called a parallel plate capacitor. It is easy to see the relationship between the voltage and the stored charge for a parallel plate capacitor, as shown in this figure. Each electric field line starts on an individual positive charge and ends on a negative one, so that there will be more field lines if there is more charge. (Drawing a single field line per charge is a convenience, only. We can draw many field lines for each charge, but the total number is proportional to the number of charges.) The electric field strength is, thus, directly proportional to \(Q\).

The field is proportional to the charge:

\(E\propto Q,\)

where the symbol \(\propto \) means “proportional to.” From the discussion in Electric Potential in a Uniform Electric Field, we know that the voltage across parallel plates is \(V=\text{Ed}\). Thus,

\(V\propto E.\)

It follows, then, that \(\mathrm{V \propto }\phantom{\rule{0.25em}{0ex}}Q\), and conversely,

\(Q\propto V.\)

This is true in general: The greater the voltage applied to any capacitor, the greater the charge stored in it.

Different capacitors will store different amounts of charge for the same applied voltage, depending on their physical characteristics. We define their capacitance \(C\) to be such that the charge \(Q\) stored in a capacitor is proportional to \(C\). The charge stored in a capacitor is given by

\(Q=\text{CV}.\)

This equation expresses the two major factors affecting the amount of charge stored. Those factors are the physical characteristics of the capacitor, \(C\), and the voltage, \(V\). Rearranging the equation, we see that capacitance \(C\) is the amount of charge stored per volt, or

\(C=\cfrac{Q}{V}.\)

The unit of capacitance is the farad (F), named for Michael Faraday (1791–1867), an English scientist who contributed to the fields of electromagnetism and electrochemistry. Since capacitance is charge per unit voltage, we see that a farad is a coulomb per volt, or

\(\text{1 F}=\cfrac{\text{1 C}}{\text{1 V}}.\)

A 1-farad capacitor would be able to store 1 coulomb (a very large amount of charge) with the application of only 1 volt. One farad is, thus, a very large capacitance. Typical capacitors range from fractions of a picofarad \((1 pF={\text{10}}^{\text{–12}}\phantom{\rule{0.25em}{0ex}}\text{F})\) to millifarads \((1 mF={\text{10}}^{–3}\phantom{\rule{0.25em}{0ex}}\text{F})\).

This figure shows some common capacitors. Capacitors are primarily made of ceramic, glass, or plastic, depending upon purpose and size. Insulating materials, called dielectrics, are commonly used in their construction, as discussed below.