Physics
Capacitance
Capacitance is a measure of a system's ability to store electric charge. It is determined by the ratio of the magnitude of the stored charge to the electric potential difference across the system. Capacitance is a fundamental property in electrical circuits and is represented by the symbol C, measured in farads (F).
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10 Key excerpts on "Capacitance"
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- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
The magnitude of the electrical field in the space between the parallel plates is E = σ/ε 0 , where σ denotes the surface charge density on one plate (recall that σ is the charge Q per the surface area A). Thus, the magnitude of the field is directly proportional to Q. 346 Chapter 8 | Capacitance This OpenStax book is available for free at http://cnx.org/content/col12074/1.3 Figure 8.3 The charge separation in a capacitor shows that the charges remain on the surfaces of the capacitor plates. Electrical field lines in a parallel-plate capacitor begin with positive charges and end with negative charges. The magnitude of the electrical field in the space between the plates is in direct proportion to the amount of charge on the capacitor. Capacitors with different physical characteristics (such as shape and size of their plates) store different amounts of charge for the same applied voltage V across their plates. The Capacitance C of a capacitor is defined as the ratio of the maximum charge Q that can be stored in a capacitor to the applied voltage V across its plates. In other words, Capacitance is the largest amount of charge per volt that can be stored on the device: (8.1) C = Q V . The SI unit of Capacitance is the farad (F), named after Michael Faraday (1791–1867). Since Capacitance is the charge per unit voltage, one farad is one coulomb per one volt, or 1 F = 1C 1V . By definition, a 1.0-F capacitor is able to store 1.0 C of charge (a very large amount of charge) when the potential difference between its plates is only 1.0 V. One farad is therefore a very large Capacitance. Typical Capacitance values range from picofarads (1 pF = 10 −12 F) to millifarads (1 mF = 10 −3 F) , which also includes microfarads ( 1 µF = 10 −6 F ). Capacitors can be produced in various shapes and sizes (Figure 8.4). Chapter 8 | Capacitance 347 Figure 8.4 These are some typical capacitors used in electronic devices. A capacitor’s size is not necessarily related to its Capacitance value.
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.
- Jerry D. Wilson, Anthony J. Buffa, Bo Lou(Authors)
- 2022(Publication Date)
- CRC Press(Publisher)
Capacitance represents the charge Q that can be stored per volt. If a capacitor has a large Capacitance value, this means it is capable of holding a large charge per volt compared to one of smaller Capacitance. Thus if you connect the same battery to two different capacitors, the one with the larger Capacitance stores more charge and energy. Capacitance depends only on the geometry (size, shape, and spacing) of the plates (and possibly any material between the plates – see Section 16.5) but specifically not the charge on the plates. To understand this, consider again a set of parallel plates which is now called a parallel plate capacitor. The electric field between the plates given by Equation 16.5: E kQ A = 4π The potential difference between the plates can be computed from Equation 16.2 as follows: ΔV Ed kQd A = = 4π The Capacitance of a parallel plate arrangement is then C Q V k A d = = ⎛ ⎝ ⎜ ⎜ ⎜ ⎞ ⎠ ⎟ ⎟ ⎟ ⎟ Δ 1 4π ( ) parallel plates only (16.10) It is common to replace the constants in the parentheses in Equation 16.10 with a single constant called the permittivity of free space ( ε o ). Knowing k, the permittivity has a value of ε π o 2 C N m (permittivity of free space = = × ⋅ − 1 4 8 85 10 12 2 k . ) (16.11) ε o describes the electrical properties of free space (vacuum), but its value in air is only 0.05% larger. In our calculations, they will be taken to be the same. It is common to rewrite Equation 16.10 in terms of ε o : C A d = ε o (parallel plates only) (16.12) The next Example shows just how unrealistically large an air- filled capacitor with a Capacitance of 1.0 F would be. EXAMPLE 16.6: PARALLEL PLATE CAPACITORS – HOW LARGE IS A FARAD? What must the plate area for an air-filled parallel plate capacitor be in order for it to have a Capacitance of 1.0 F, if the plate separa- tion is 1.0 mm? Would it be realistic to consider building such a capacitor? THINKING IT THROUGH. The area can be calculated directly from Equation 16.12.
- 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)
CHAPTER 25 Capacitance 25.1 Capacitance LEARNING OBJECTIVES After reading this module, you should be able to: 25.1.1 sketch a schematic diagram of a circuit with a parallel‐plate capacitor, a battery, and an open or closed switch 25.1.2 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 25.1.3 for a capacitor, apply the relationship between the magnitude of charge q on either plate (‘the charge on the capacitor’), the potential difference V between the plates (‘the potential across the capacitor’), and the Capacitance C of the capacitor. KEY IDEAS • A capacitor consists of two isolated conductors (the plates) with charges +q and −q. Its Capacitance C is defned from q = CV, where V is the potential difference between the plates. • When a circuit with a battery, an open switch, and an uncharged capacitor is completed by closing the switch, conduction electrons shift, leaving the capacitor plates with opposite charges. Why study physics? People in Australia and New Zealand who install timber flooring deal with many consumer complaints arising from moisture problems. Capacitance moisture meters determine the amount of moisture in the timber based upon the change in the dielectric constant of the timber. This varies with timber density and moisture content. 1 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. 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.
eBook - PDF- Mike Tooley, Lloyd Dingle(Authors)
- 2010(Publication Date)
- Routledge(Publisher)
mA From which i 8 8 10 8 8 3 . . A mA Charge, Capacitance and voltage The charge or quantity of electricity that can be stored in the electric field between the capacitor plates is proportional to the applied voltage and the Capacitance of the capacitor (see Figure 6.62 ). Thus, Q CV where Q is the charge (coulombs), C is the Capacitance (F) and V is the potential difference (V). Example 6.33 A 10 μF capacitor is charged to a potential of 250V. Determine the charge stored. The charge stored will be given by: Q CV 10 10 250 2 5 6 . mC KEY POINT Charge is the quantity of electricity that can be stored in a capacitor. The charge in a capacitor is directly proportional to the product of the Capacitance and the applied potential difference TYK 6.19 Determine the charge in a capacitor of 470 μF when a potential difference of 22 V appears across its plates. T e s t y o u r k n o w l e d g e TYK Electrical and Electronic Principles 491 UNIT 6 Energy storage When charge, Q, is plotted against voltage, V, for a particular value of Capacitance, C, it follows the linear law shown in Figure 6.63a. The slope of the line ( Q/V) indicates the Capacitance whilst the area below the line (shown as shaded portion in Figure 6.63b) is a measure of the energy stored in the capacitor. The larger this area is the more energy is stored. TYK 6.20 A capacitor of 150 μF is required to store a charge of 400 μC. What voltage should be applied to the capacitor? Supply, V Field lines Capacitance, C Potential difference, V Charge, Q 1 Figure 6.62 Capacitance, charge and voltage Charge, Q High Capacitance Low Capacitance Voltage, V (a) Slope Q V C (b) Charge V Voltage Q Energy 1 2 QV Figure 6.63 Charge plotted against voltage for a capacitor In Figure 6.63, the shaded area can be found by considering the area to be a triangle in which the area is the product of half the base and the height.
eBook - PDFFundamentals of Electromagnetics
1Internal Behavior of Lumped Elements
- David Voltmer(Author)
- 2022(Publication Date)
- Springer(Publisher)
91 C H A P T E R 2 Capacitors 2.1 CAPACITORS: A FIRST GLANCE The basic function of a capacitor is as a storage element for electric energy. Its configuration is designed to enhance this function. Properly selected materials minimize its power dissipation as well. As you recall from circuits, the terminal behavior of an ideal capacitor is given by I C = C dV C dt (2.1) where I C is the current flowing into the capacitor in the direction of the voltage drop across the capacitor, V C , and C is the Capacitance value of the capacitor expressed in Farads and abbreviated as F . Its terminal behavior is more complicated than that of a resistor due to the presence of the derivative of voltage. As with resistors, we will investigate the internal, electromagnetic behavior of capacitors to better understand them. The simplest capacitor configuration has many similarities with that of resistors, see Fig. 2.1. Two metallic wire leads provide the connection between a capacitor and the external circuit. Current enters the element at one end through the wire lead and flows directly onto a metallic electrode. An equal current flows from the other electrode out of the capacitor via the other wire lead. The flux guiding material is located between the two metal electrodes. An insulator serves as the electric flux guide in a capacitor similar to the way conductive material in a resistor guides the current flux. The charges that enter the capacitor do not flow to the opposite electrode and leave via the other lead because the conductivity of the insulator is zero. Instead, they accumulate on the electrode while an equal charge flows from the other electrode out of the other wire lead. This leaves equal but opposite charges on the two electrodes. The use of an insulating flux guide instead of one that is conductive is the chief reason for the marked difference in behavior between capacitors and resistors.
eBook - ePub- Adrian Waygood(Author)
- 2018(Publication Date)
- Routledge(Publisher)
Chapter 22 CapacitanceObjectives
On completion of this chapter, you should be able to- explain the primary function of a capacitor.
- describe the essential components of any capacitor.
- describe the charging/discharging process of a capacitor.
- describe what is meant by ‘the charge on a capacitor’.
- describe how electric charge behaves with capacitors connected in series.
- recognise the circuit symbols for different types of capacitor.
- state the unit of measurement for Capacitance.
- list the factors that affect Capacitance, and their relationship.
- describe how a capacitor’s dielectric affects Capacitance of that capacitor.
- describe the relationship between absolute permittivity, the permittivity of free space, and relative permittivity.
- determine the energy stored by a capacitor.
- describe the basic construction of practical fixed-value and variable-value capacitors.
- solve simple problems on the time constant of a resistive-capacitive circuit.
- solve simple series, parallel and series-parallel capacitive circuits.
Introduction
In 1745, barely three years before his death, a German cleric and physicist Ewald Georg von Kleist (1700–1748) invented a device for ‘storing static electricity’ for the purpose of his experiments. It consisted of a glass jar, coated both inside and out with metal foil (often, gold leaf), and with its inner coating connected, via a metal chain, to a brass rod that passed through an insulated wooden stopper – as illustrated in Figure 22.1
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