Capacitance and Dielectrics
CHAPTE R OUTLI 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
L All of these devices are capacitors, which store electric charge and energy. Acapacitor is
one type of circuit element that we can combine with others to make electric circuits. (Paul Silverman/Fundamental Photographs)
In 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 usein current society. We shall discuss capacitors— devices that store electric charge. This discussion will be followed by the study of resistors 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 frequencyof 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.
Figure 26.1 A capacitor consists oftwo conductors. When the capacitor is charged, the conductors carry charges of equal magnitude and opposite sign.
Deﬁnition of Capacitance
26.1 Capacitance Is a Capacity
To understand capacitance, think of similar notions that use a similar word. The capacity of a milk carton is the volume of milk that it can store. The heat capacity of an object is theamount of energy an object can store per unit of temperature difference. The capacitance of a capacitor is the amount of charge the capacitor can store per unit of potential difference.
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 calledplates. A potential difference V exists between the conductors 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 capacitor1 is linearly proportional to the potential difference between the conductors; that is, Q V. The proportionality constant depends on the shape andseparation of the conductors.2 We can write this relationship as Q C V if we deﬁne capacitance as follows:
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: C Q V (26.1)
Although the total charge on the capacitor is zero (because there is as much excess positive chargeon 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.’’
The proportionality between V and Q can be proved from Coulomb’s law or by experiment.
S ECTI O N 26.2 • Calculating Capacitance
Note that by deﬁnition capacitance is always a positivequantity. Furthermore, the charge Q and the potential difference V are always expressed in Equation 26.1 as positive quantities. Because the potential difference increases linearly with the stored charge, the ratio Q / V is constant for a given capacitor. Therefore, capacitance is a measure of a capacitor’s ability to store charge. Because positive and negative charges are separated in the system of...