Physics
Capacitors
Capacitors are electronic components that store and release electrical energy. They consist of two conductive plates separated by an insulating material, known as a dielectric. When a voltage is applied, one plate accumulates positive charge while the other accumulates negative charge, creating an electric field between them. Capacitors are commonly used in electronic circuits for energy storage, filtering, and timing applications.
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10 Key excerpts on "Capacitors"
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
717 C H A P T E R 2 5 Capacitance What Is Physics? One goal of physics is to provide the basic science for practical devices designed by engineers. The focus of this chapter is on one extremely common example—the capacitor, a device in which electrical energy can be stored. For example, the batteries in a camera store energy in the photoflash unit by charg- ing a capacitor. The batteries can supply energy at only a modest rate, too slowly for the photoflash unit to emit a flash of light. However, once the capacitor is charged, it can supply energy at a much greater rate when the photoflash unit is triggered—enough energy to allow the unit to emit a burst of bright light. The physics of Capacitors can be generalized to other devices and to any situ- ation involving electric fields. For example, Earth’s atmospheric electric field is modeled by meteorologists as being produced by a huge spherical capacitor that partially discharges via lightning. The charge that skis collect as they slide along snow can be modeled as being stored in a capacitor that frequently discharges as sparks (which can be seen by nighttime skiers on dry snow). The first step in our discussion of Capacitors is to determine how much charge can be stored. This “how much” is called capacitance. Capacitance Figure 25-1 shows some of the many sizes and shapes of Capacitors. Figure 25-2 shows the basic elements of any capacitor — two isolated conductors of any 25-1 CAPACITANCE Learning Objectives After reading this module, you should be able to . . . 25.01 Sketch a schematic diagram of a circuit with a parallel-plate capacitor, a battery, and an open or closed switch. 25.02 In a circuit with a battery, an open switch, and an uncharged capacitor, explain what happens to the conduction electrons when the switch is closed.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
C H A P T E R 2 5 Capacitance What Is Physics? One goal of physics is to provide the basic science for practical devices designed by engineers. The focus of this chapter is on one extremely common example—the capacitor, a device in which electrical energy can be stored. For example, the batteries in a camera store energy in the photoflash unit by charging a capacitor. The batteries can supply energy at only a modest rate, too slowly for the photoflash unit to emit a flash of light. However, once the capaci- tor is charged, it can supply energy at a much greater rate when the photoflash unit is triggered—enough energy to allow the unit to emit a burst of bright light. The physics of Capacitors can be generalized to other devices and to any sit- uation involving electric fields. For example, Earth’s atmospheric electric field is modeled by meteorologists as being produced by a huge spherical capacitor that partially discharges via lightning. The charge that skis collect as they slide along snow can be modeled as being stored in a capacitor that frequently dis- charges as sparks (which can be seen by nighttime skiers on dry snow). The first step in our discussion of Capacitors is to determine how much charge can be stored. This “how much” is called capacitance. Capacitance Figure 25-1 shows some of the many sizes and shapes of Capacitors. Figure 25-2 shows the basic elements of any capacitor — two isolated conductors 25-1 CAPACITANCE Learning Objectives After reading this module, you should be able to . . . 25.01 Sketch a schematic diagram of a circuit with a parallel-plate capacitor, a battery, and an open or closed switch. 25.02 In a circuit with a battery, an open switch, and an uncharged capacitor, explain what happens to the conduction electrons when the switch is closed.
eBook - PDF- David Halliday, Robert Resnick, Kenneth S. Krane(Authors)
- 2019(Publication Date)
- Wiley(Publisher)
CHAPTER 30 679 CHAPTER 30 CAPACITANCE I n many applications of electric circuits, the goal is to store electrical charge or energy in an electrostatic field. A device that stores charge is called a capacitor, and the property that determines how much charge it can store is its capacitance. We shall see that the ca- pacitance depends on the geometrical properties of the device and not on the electric field or the potential. In this chapter we define capacitance and show how to calculate the capacitance of a few simple de- vices and of combinations of Capacitors. We study the energy stored in Capacitors and show how it is re- lated to the strength of the electric field. Finally, we investigate how the presence of a dielectric in a capaci- tor enhances its ability to store electric charge. 30-1 Capacitors A capacitor* is a device that stores energy in an electrosta- tic field. A flashbulb, for example, requires a short burst of electric energy that exceeds what a battery can generally provide. A capacitor can draw energy relatively slowly (over several seconds) from the battery, and it then can re- lease the energy rapidly (within milliseconds) through the bulb. Much larger Capacitors are used to produce short laser pulses in attempts to induce thermonuclear fusion in tiny pellets of hydrogen. In this case the power level during the pulse is about 10 14 W, about 200 times the entire electrical generating capacity of the United States, but the pulses typ- ically last only for 10 9 s. Capacitors are also used to produce electric fields, such as the parallel-plate device that gives the very nearly uni- form electric field that deflects beams of electrons in a TV or oscilloscope tube. In circuits, Capacitors are often used to smooth out the sudden variations in line voltage that can damage computer memories. In another application, the tuning of a radio or TV receiver is usually done by varying the capacitance of the circuit.
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
The physics of Capacitors can be generalized to other devices and to any situation involving electric fields. For example, Earth’s atmo- spheric electric field is modeled by meteorologists as being produced by a huge spherical capacitor that partially discharges via lightning. The charge that skis collect as they slide along snow can be modeled as being stored in a capacitor that frequently discharges as sparks (which can be seen by nighttime skiers on dry snow). The first step in our discussion of Capacitors is to determine how much charge can be stored. This “how much” is called capacitance. Capacitance Figure 25.1.1 shows some of the many sizes and shapes of Capacitors. Figure 25.1.2 shows the basic elements of any capacitor—two isolated conductors of any shape. No matter what their geometry, flat or not, we call these conductors plates. Figure 25.1.1 An assortment of Capacitors. Paul Silvermann/Fundamental Photographs 760 CHAPTER 25 CAPACITANCE Figure 25.1.3a shows a less general but more conventional arrangement, called a parallel-plate capacitor, consisting of two parallel conducting plates of area A separated by a distance d. The symbol we use to represent a capacitor (⫞⊦) is based on the structure of a parallel-plate capacitor but is used for Capacitors of all geometries. We assume for the time being that no material medium (such as glass or plastic) is present in the region between the plates. In Module 25.5, we shall remove this restriction. When a capacitor is charged, its plates have charges of equal magnitudes but opposite signs: +q and –q. However, we refer to the charge of a capacitor as being q, the absolute value of these charges on the plates. (Note that q is not the net charge on the capacitor, which is zero.) Because the plates are conductors, they are equipotential surfaces; all points on a plate are at the same electric potential. Moreover, there is a potential dif- ference between the two plates.
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
8 | CAPACITANCE Figure 8.1 The tree-like branch patterns in this clear Plexiglas® block are known as a Lichtenberg figure, named for the German physicist Georg Christof Lichtenberg (1742–1799), who was the first to study these patterns. The “branches” are created by the dielectric breakdown produced by a strong electric field. (credit: modification of work by Bert Hickman) Chapter Outline 8.1 Capacitors and Capacitance 8.2 Capacitors in Series and in Parallel 8.3 Energy Stored in a Capacitor 8.4 Capacitor with a Dielectric 8.5 Molecular Model of a Dielectric Introduction Capacitors are important components of electrical circuits in many electronic devices, including pacemakers, cell phones, and computers. In this chapter, we study their properties, and, over the next few chapters, we examine their function in combination with other circuit elements. By themselves, Capacitors are often used to store electrical energy and release it when needed; with other circuit components, Capacitors often act as part of a filter that allows some electrical signals to pass while blocking others. You can see why Capacitors are considered one of the fundamental components of electrical circuits. 8.1 | Capacitors and Capacitance Learning Objectives By the end of this section, you will be able to: • 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, Chapter 8 | Capacitance 345 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.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
____________________ WORLD TECHNOLOGIES ____________________ Chapter 9 Capacitor Capacitor Modern Capacitors, by a cm rule Type Passive Invented Ewald Georg von Kleist (October 1745) Electronic symbol A capacitor (formerly known as condenser ) is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator). When there is a potential difference (voltage) across the conductors, a static electric field develops in the dielectric that stores energy and produces a mechanical force between the conductors. An ideal capacitor is characterized by a single constant value, capacitance, measured in farads. This is the ratio of the electric charge on each conductor to the potential difference between them. Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass, in filter networks, for smoothing the output of power supplies, in the resonant circuits that tune radios to particular frequencies and for many other purposes. ____________________ WORLD TECHNOLOGIES ____________________ A typical electrolytic capacitor The effect is greatest when there is a narrow separation between large areas of conductor, hence capacitor conductors are often called plates, referring to an early means of construction. In practice the dielectric between the plates passes a small amount of leakage current and also has an electric field strength limit, resulting in a breakdown voltage, while the conductors and leads introduce an undesired inductance and resistance. ____________________ WORLD TECHNOLOGIES ____________________ History Battery of four Leyden jars in Museum Boerhaave, Leiden, the Netherlands. In October 1745, Ewald Georg von Kleist of Pomerania in Germany found that charge could be stored by connecting a high voltage electrostatic generator by a wire to a volume of water in a hand-held glass jar.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Orange Apple(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 1 Capacitor Capacitor Modern Capacitors, by a cm rule Type Passive Invented Ewald Georg von Kleist (October 1745) Electronic symbol A capacitor (formerly known as condenser ) is a passive electronic component consisting of a pair of conductors separated by a dielectric (insulator). When there is a potential difference (voltage) across the conductors, a static electric field develops in the dielectric that stores energy and produces a mechanical force between the conductors. An ideal capacitor is characterized by a single constant value, capacitance, measured in farads. This is the ratio of the electric charge on each conductor to the potential difference between them. Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass, in filter networks, for smoothing the output of power supplies, in the resonant circuits that tune radios to particular frequencies and for many other purposes. ________________________ WORLD TECHNOLOGIES ________________________ A typical electrolytic capacitor The effect is greatest when there is a narrow separation between large areas of conductor, hence capacitor conductors are often called plates, referring to an early means of construction. In practice the dielectric between the plates passes a small amount of leakage current and also has an electric field strength limit, resulting in a breakdown voltage, while the conductors and leads introduce an undesired inductance and resistance. ________________________ WORLD TECHNOLOGIES ________________________ History Battery of four Leyden jars in Museum Boerhaave, Leiden, the Netherlands. In October 1745, Ewald Georg von Kleist of Pomerania in Germany found that charge could be stored by connecting a high voltage electrostatic generator by a wire to a volume of water in a hand-held glass jar.
- David Halliday, Jearl Walker, Patrick Keleher, Paul Lasky, John Long, Judith Dawes, Julius Orwa, Ajay Mahato, Peter Huf, Warren Stannard, Amanda Edgar, Liam Lyons, Dipesh Bhattarai(Authors)
- 2020(Publication Date)
- Wiley(Publisher)
The first step in our discussion of Capacitors is to determine how much charge can be stored. This ‘how much’ is called capacitance. Capacitance Figure 25.1 shows some of the many sizes and shapes of Capacitors. Figure 25.2 shows the basic elements of any capacitor — two isolated conductors of any shape, which, flat or not, are called plates. Figure 25.3 shows two views of a less general but more conventional arrangement, called a parallel‐plate capacitor, consisting of two parallel conducting plates of area A separated by a distance d. Pdf_Folio:547 FIGURE 25.1 An assortment of Capacitors. Paul Silvermann / Fundamental Photographs FIGURE 25.2 Two conductors, isolated electrically from each other and from their surroundings, form a capacitor. When the capacitor is charged, the charges on the conductors, or plates as they are called, have the same magnitude q but opposite signs. +q - q FIGURE 25.3 (a) A parallel-plate capacitor, made up of two plates of area A separated by a distance d. The charges on the facing plate surfaces have the same magnitude q but opposite signs. (b) As the feld lines show, the electric feld due to the charged plates is uniform in the central region between the plates. The feld is not uniform at the edges of the plates, as indicated by the ‘fringing’ of the feld lines there. Area A V d Top side of bottom plate has charge -q A -q +q (b) (a ) Bottom side of top plate has charge +q Electric field lines We assume for the time being that no material medium (such as glass or plastic) is present in the region between the plates. In module 25.5, we will remove this restriction. When a capacitor is charged, its plates have charges of equal magnitudes but opposite signs: +q and −q. However, we refer to the charge of a capacitor as being q, the absolute value of these charges on the plates.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- White Word Publications(Publisher)
The conductors thus hold equal and opposite charges on their facing surfaces, and the dielectric develops an electric field. In SI units, a capacitance of one farad means that one coulomb of charge on each conductor causes a voltage of one volt across the device. The capacitor is a reasonably general model for electric fields within electric circuits. An ideal capacitor is wholly characterized by a constant capacitance C , defined as the ratio of charge ± Q on each conductor to the voltage V between them: Sometimes charge build-up affects the capacitor mechanically, causing its capacitance to vary. In this case, capacitance is defined in terms of incremental changes: ____________________ WORLD TECHNOLOGIES ____________________ Energy storage Work must be done by an external influence to move charge between the conductors in a capacitor. When the external influence is removed the charge separation persists in the electric field and energy is stored to be released when the charge is allowed to return to its equilibrium position. The work done in establishing the electric field, and hence the amount of energy stored, is given by: Current-voltage relation The current i ( t ) through any component in an electric circuit is defined as the rate of flow of a charge q ( t ) passing through it, but actual charges, electrons, cannot pass through the dielectric layer of a capacitor, rather an electron accumulates on the negative plate for each one that leaves the positive plate, resulting in an electron depletion and consequent positive charge on one electrode that is equal and opposite to the accumulated negative charge on the other. Thus the charge on the electrodes is equal to the integral of the current as well as proportional to the voltage as discussed above. As with any antiderivative, a constant of integration is added to represent the initial voltage v ( t 0 ). This is the integral form of the capacitor equation, .
eBook - PDFNewnes Circuit Calculations Pocket Book
with Computer Programs
- Thomas J. Davies(Author)
- 2016(Publication Date)
- Newnes(Publisher)
Capacitance is a measure of how much charge can be stored for each volt across the capacitor. Charge Q = CV where Q is in coulombs, C C is in farads, F V is in volts, V Example 7 A 680 pF capacitor has 6 V across the plates. Calculate the charge stored. Q = CV = 680 x 10 12 x 6 = 4.08 x 1 0 -9 C = 4.08 x 10~ 9 x 10 9 nC = 4.08 nC 10 PRINT PROG 73 20 PRINT CAPACITOR CHARGE 30 INPUT ENTER CAPACITANCE IN PICOFARADS ; C 40 INPUT ENTER VOLTAGE IN VOLTS ; V 50 LET C=C/10*12 60 LET Q=C*V 70 PRINT CHARGE = Q*10*9 NANOCOULOMDS Example 8 A 0.1 uF capacitor stores a charge of 0.02 x 10 3 C. What is the voltage across the terminals? Capacitors 107 y = Q _ 0-02 x 1Q-3 _ O02 x 10 3 0.1 x 10 = 200 V 0.1 10 PRINT PROG 74 20 PRINT CAPACITOR VOLTAGE 30 INPUT ENTER CAPACITANCE IN MICROFARADS ; C 40 INPUT ENTER CHARGE IN COULOMBS ; Q 50 LET C=C/1CT6 60 LET V=Q/C 70 PRINT VOLTAGE = V VOLTS Example 9 Calculate the value of a capacitor which stores a charge of 2 mC when charged to 400 V. Q 2 x 10~ 3 2 x KT 3 x 10 6 C = — = F = ixF V 400 400 = 5 (JL F 10 PRINT PROG 7 5 20 PRINT CAPACITOR VALUE 30 INPUT ENTER CHARGE IN MILLICOULOMBS ; Q 40 INPUT ENTER VOLTAGE IN VOLTS ; V 50 LET Q=Q/10*3 60 LET C=Q/V 70 PRINT VALUE = C*10*6 MICROFARADS (c) Energy stored When charge is moved into a capacitor work is done, and hence energy is expended. This energy is stored between the plates in the form of an electric field. Energy stored, W = CV 2 where W is in joules, J C is in farads, F V is in volts, V Example 10 Calculate the energy stored in a 0.1 u-F capacitor with an applied voltage of 250 V. W = x 0.1 x 10~ 6 x (250) 2 = 3.125 x KT 3 J = 3.125 x 10 3 x 10 3 = 3.125 mJ 10 PRINT PROG 76 20 PRINT ENERGY STORED 30 INPUT ENTER CAPACITANCE IN MICROFARADS ; C 40 INPUT ENTER VOLTAGE IN VOLTS ; V 50 LET C=C/10*6 60 LET W=.5*C*V*2 70 PRINT ENERGY STORED = WM0~3 MILLIJOULES Example 11 The energy stored in a 0.25 |xF capacitor is 8 x 10 4 J. What is the terminal voltage?
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