795795795Capacitance and DielectricsCHAPTER OUTLINE26.1Deﬁnition of Capacitance26.2Calculating Capacitance26.3Combinations of Capacitors26.4Energy Stored in a ChargedCapacitor26.5Capacitors with Dielectrics26.6Electric Dipole in an ElectricField26.7An Atomic Description ofDielectrics±All of these devices are capacitors, which store electric charge and energy. A capacitor isone type of circuit element that we can combine with others to make electric circuits.(Paul Silverman/Fundamental Photographs)Chapter 26
796In this chapter, we will introduce the ﬁrst of three simple circuit elementsthat can beconnected with wires to form an electric circuit. Electric circuits are the basis for thevast 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-torsin Chapter 27 and inductorsin Chapter 32. In later chapters, we will study moresophisticated circuit elements such as diodesand transistors.Capacitors are commonly used in a variety of electric circuits. For instance, they areused to tune the frequency of radio receivers, as ﬁlters in power supplies, to eliminatesparking in automobile ignition systems, and as energy-storing devices in electronicﬂash units.A capacitor consists of two conductors separated by an insulator. The capacitanceof a given capacitor depends on its geometry and on the material—called a dielectric—that separates the conductors.26.1Deﬁnition of CapacitanceConsider two conductors carrying charges of equal magnitude and opposite sign, asshown in Figure 26.1. Such a combination of two conductors is called a capacitor.The conductors are called plates.A potential difference ±Vexists 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 givenvoltage? Experiments show that the quantity of charge Qon a capacitor1is linearlyproportional to the potential difference between the conductors; that is, Q²±V.The proportionality constant depends on the shape and separation of the con-ductors.2We can write this relationship as Q³C±Vif we deﬁne capacitance asfollows:The capacitanceCof a capacitor is deﬁned as the ratio of the magnitude of thecharge on either conductor to the magnitude of the potential difference betweenthe conductors:(26.1)C±Q±V–Q+QFigure 26.1A capacitor consists oftwo conductors. When the capaci-tor is charged, the conductors carrycharges of equal magnitude andopposite sign.±PITFALL PREVENTION 26.1Capacitance Is aCapacityTo understand capacitance, thinkof similar notions that use a simi-lar word. The capacityof a milkcarton is the volume of milk thatit can store. The heatcapacityofan object is the amount of energyan object can store per unitof temperature difference. Thecapacitanceof a capacitor is theamount of charge the capacitorcan store per unit of potentialdifference.
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