26 - capacitance

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Unformatted text preview: 795 795 795 Capacitance and Dielectrics C HAP TE R O UTL I N E 26.1 Definition of Capacitance 26.2 Calculating Capacitance 26.3 Combinations of Capacitors 26.4 Energy Stored in a Charged Capacitor 26.5 Capacitors with Dielectrics 26.6 Electric Dipole in an Electric Field 26.7 An Atomic Description of Dielectrics All of these devices are capacitors, which store electric charge and energy. A capacitor is one type of circuit element that we can combine with others to make electric circuits. (Paul Silverman/Fundamental Photographs) Chapter 26 796 I n this chapter, we will introduce the first of three simple circuit elements that can be connected with wires to form an electric circuit. Electric circuits are the basis for the vast majority of the devices that we use in current society. We shall discuss capacitors — devices that store electric charge. This discussion will be followed by the study of resis- tors in Chapter 27 and inductors in Chapter 32. In later chapters, we will study more sophisticated circuit elements such as diodes and transistors . Capacitors are commonly used in a variety of electric circuits. For instance, they are used to tune the frequency of radio receivers, as filters in power supplies, to eliminate sparking in automobile ignition systems, and as energy-storing devices in electronic flash units. A capacitor consists of two conductors separated by an insulator. The capacitance of a given capacitor depends on its geometry and on the material—called a dielectric — that separates the conductors. 26.1 Definition of Capacitance Consider two conductors carrying charges of equal magnitude and opposite sign, as shown in Figure 26.1. Such a combination of two conductors is called a capacitor. The conductors are called plates. A potential difference V exists between the con- ductors due to the presence of the charges. What determines how much charge is on the plates of a capacitor for a given voltage? Experiments show that the quantity of charge Q on a capacitor 1 is linearly proportional to the potential difference between the conductors; that is, Q V . The proportionality constant depends on the shape and separation of the con- ductors. 2 We can write this relationship as Q C V if we define capacitance as follows: 1 Although the total charge on the capacitor is zero (because there is as much excess positive charge on one conductor as there is excess negative charge on the other), it is common practice to refer to the magnitude of the charge on either conductor as “the charge on the capacitor.’’ 2 The proportionality between V and Q can be proved from Coulomb’s law or by experiment. The capacitance C of a capacitor is defined as the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between the conductors: (26.1) C Q V – Q + Q Figure 26.1 A capacitor consists of two conductors. When the capaci- tor is charged, the conductors carry charges of equal magnitude and opposite sign.opposite sign....
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