4.1 Capacitors and Capacitance
LEARNING OBJECTIVES
- Explain the concepts of a capacitor and its capacitance
- Describe how to evaluate the capacitance of a system of conductors
A capacitor is a device used to store electrical charge and electrical energy. It consists of at least two electrical conductors separated by a distance. (Note that such electrical conductors are sometimes referred to as “electrodes,” but more correctly, they are “capacitor plates.”) The space between capacitors may simply be a vacuum, and, in that case, a capacitor is then known as a “vacuum capacitor.” However, the space is usually filled with an insulating material known as a dielectric. (You will learn more about dielectrics in the sections on dielectrics later in this chapter.) The amount of storage in a capacitor is determined by a property called capacitance, which you will learn more about a bit later in this section.
Capacitors have applications ranging from filtering static from 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 Figure 4.1.1. Most of the time, a dielectric is used between the two plates. When battery terminals are connected to an initially uncharged capacitor, the battery potential moves a small amount of charge of magnitude from the positive plate to the negative plate. The capacitor remains neutral overall, but with charges and residing on opposite plates.
(Figure 4.1.1)
A system composed of two identical parallel-conducting plates separated by a distance is called a parallel-plate capacitor (Figure 4.1.2). The magnitude of the electrical field in the space between the parallel plates is , where denotes the surface charge density on one plate (recall that is the charge per the surface area ). Thus, the magnitude of the field is directly proportional to .
(Figure 4.1.2)
Capacitors with different physical characteristics (such as shape and size of their plates) store different amounts of charge for the same applied voltage across their plates. The capacitance of a capacitor is defined as the ratio of the maximum charge that can be stored in a capacitor to the applied voltage across its plates. In other words, capacitance is the largest amount of charge per volt that can be stored on the device:
The SI unit of capacitance is the farad (), named after Michael Faraday (1791–1867). Since capacitance is the charge per unit voltage, one farad is one coulomb per one volt, or
By definition, a capacitor is able to store of charge (a very large amount of charge) when the potential difference between its plates is only . One farad is therefore a very large capacitance. Typical capacitance values range from picofarads () to millifarads (), which also includes microfarads (). Capacitors can be produced in various shapes and sizes (Figure 4.1.3).
(Figure 4.1.3)
Calculation of Capacitance
We can calculate the capacitance of a pair of condu