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 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 situation 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 After reading this module, you should be able to . . . 25.01 Sketch a schematic diagram of a circuit with a parallelplate 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. 25.03 For a capacitor, apply the relationship between the magnitude of charge q on either plate (“the charge on the capacitor”)is completed by closing the switch, conduction electrons shift, leaving the capacitor plates with opposite charges. Learning Objectives Key Ideas 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. Figure 25-1 An assortment of capacitors. +q –q Paul Silvermann/Fundamental Photographs 718 CHAPTER 25 CAPACITANCE Figure 25-4 (a) Battery B, switch S, and plates h and l of capacitor C, connected in a circuit. (b) A schematic diagram with the circuit elements represented by their symbols. l V + – (b) C B Terminal S (a) + – B S h l C h Terminal shape. No matter what their geometry, flat or not, we call these conductors plates. Figure 25-3a 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 difference between the two plates. For historical reasons, we represent the absolute value of this potential difference with V rather than with the V we used in previous notation. The charge q and the potential difference V for a capacitor are proportional to each other; that is, q CV. (25-1) The proportionality constant C is called the capacitance of the capacitor. Its value depends only on the geometry of the plates and not on their charge or potential difference. The capacitance is a measure of how much charge must be put on the plates to produce a certain potential difference between them: The greater the capacitance, the more charge is required. The SI unit of capacitance that follows from Eq. 25-1 is the coulomb per volt. This unit occurs so often that it is given a special name, the farad (F): 1 farad 1 F 1 coulomb per volt 1 C/V. (25-2) As you will see, the farad is a very large unit. Submultiples of the farad, such as the microfarad (1 mF 106 F) and the picofarad (1 pF 1012 F), are more convenient units in practice. Charging a Capacitor One way to charge a capacitor is to place it in an electric circuit with a battery. An electric circuit is a path through which charge can flow. A battery is a device that maintains a certain potential difference between its terminals (points at which charge can enter or leave the battery) by means of internal electrochemical reactions in which electric forces can move internal charge. In Fig. 25-4a, a battery B, a switch S, an uncharged capacitor C, and interconnecting wires form a circuit. The same circuit is shown in the schematic diagram of Fig. 25-4b, in which the symbols for a battery, a switch, and a capacitor represent those devices. The battery maintains potential difference V between its terminals. The terminal of higher potential is labeled  and is often called the positive terminal; the terminal of lower potential is labeled  and is often called the negative terminal. 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 field lines show, the electric field due to the charged plates is uniform in the central region between the plates.The field is not uniform at the edges of the plates, as indicated by the “fringing” of the field lines there. Area A V d Top side of bottom plate has charge –q A –q +q (a) (b) Bottom side of top plate has charge +q Electric field lines 719 The circuit shown in Figs. 25-4a and b is said to be incomplete because switch S is open; that is, the switch does not electrically connect the wires attached to it. When the switch is closed, electrically connecting those wires, the circuit is complete and charge can then flow through the switch and the wires. As we discussed in Chapter 21, the charge that can flow through a conductor, such as a wire, is that of electrons. When the circuit of Fig. 25-4 is completed, electrons are driven through the wires by an electric field that the battery sets up in the wires. The field drives electrons from capacitor plate h to the positive terminal of the battery; thus, plate h, losing electrons, becomes positively charged. The field drives just as many electrons from the negative terminal of the battery to capacitor plate l; thus, plate l, gaining electrons, becomes negatively charged just as much as plate h, losing electrons, becomes positively 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 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 situation 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 After reading this module, you should be able to . . . 25.01 Sketch a schematic diagram of a circuit with a parallelplate 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. 25.03 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. ● A capacitor consists of two isolated conductors (the plates) with charges q and q. Its capacitance C is defined 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. Learning Objectives Key Ideas 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. Figure 25-1 An assortment of capacitors. +q –q Paul Silvermann/Fundamental Photographs 718 CHAPTER 25 CAPACITANCE Figure 25-4 (a) Battery B, switch S, and plates h and l of capacitor C, connected in a circuit. (b) A schematic diagram with the circuit elements represented by their symbols. l V + – (b) C B Terminal S (a) + – B S h l C h Terminal shape. No matter what their geometry, flat or not, we call these conductors plates. Figure 25-3a 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 difference between the two plates. For historical reasons, we represent the absolute value of this potential difference with V rather than with the V we used in previous notation. The charge q and the potential difference V for a capacitor are proportional to each other; that is, q CV. (25-1) The proportionality constant C is called the capacitance of the capacitor. Its value depends only on the geometry of the plates and not on their charge or potential difference. The capacitance is a measure of how much charge must be put on the plates to produce a certain potential difference between them: The greater the capacitance, the more charge is required. The SI unit of capacitance that follows from Eq. 25-1 is the coulomb per volt. This unit occurs so often that it is given a special name, the farad (F): 1 farad 1 F 1 coulomb per volt 1 C/V. (25-2) As you will see, the farad is a very large unit. Submultiples of the farad, such as the microfarad (1 mF 106 F) and the picofarad (1 pF 1012 F), are more convenient units in practice. Charging a Capacitor One way to charge a capacitor is to place it in an electric circuit with a battery. An electric circuit is a path through which charge can flow. A battery is a device that maintains a certain potential difference between its terminals (points at which charge can enter or leave the battery) by means of internal electrochemical reactions in which electric forces can move internal charge. In Fig. 25-4a, a battery B, a switch S, an uncharged capacitor C, and interconnecting wires form a circuit. The same circuit is shown in the schematic diagram of Fig. 25-4b, in which the symbols for a battery, a switch, and a capacitor represent those devices. The battery maintains potential difference V between its terminals. The terminal of higher potential is labeled  and is often called the positive terminal; the terminal of lower potential is labeled  and is often called the negative terminal. 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 field lines show, the electric field due to the charged plates is uniform in the central region between the plates.The field is not uniform at the edges of the plates, as indicated by the “fringing” of the field lines there. Area A V d Top side of bottom plate has charge –q A –q +q (a) (b) Bottom side of top plate has charge +q Electric field lines 719 The circuit shown in Figs. 25-4a and b is said to be incomplete because switch S is open; that is, the switch does not electrically connect the wires attached to it. When the switch is closed, electrically connecting those wires, the circuit is complete and charge can then flow through the switch and the wires. As we discussed in Chapter 21, the charge that can flow through a conductor, such as a wire, is that of electrons. When the circuit of Fig. 25-4 is completed, electrons are driven through the wires by an electric field that the battery sets up in the wires. The field drives electrons from capacitor plate h to the positive terminal of the battery; thus, plate h, losing electrons, becomes positively charged. The field drives just as many electrons from the negative terminal of the battery to capacitor plate l; thus, plate l, gaining electrons, becomes negatively charged just as much as plate h, losing electrons, becomes positively 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 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 situation 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 After reading this module, you should be able to . . . 25.01 Sketch a schematic diagram of a circuit with a parallelplate 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. 25.03 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. ● A capacitor consists of two isolated conductors (the plates) with charges q and q. Its capacitance C is defined 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. Learning Objectives Key Ideas 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. Figure 25-1 An assortment of capacitors. +q –q Paul Silvermann/Fundamental Photographs 718 CHAPTER 25 CAPACITANCE Figure 25-4 (a) Battery B, switch S, and plates h and l of capacitor C, connected in a circuit. (b) A schematic diagram with the circuit elements represented by their symbols. l V + – (b) C B Terminal S (a) + – B S h l C h Terminal shape. No matter what their geometry, flat or not, we call these conductors plates. Figure 25-3a 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 difference between the two plates. For historical reasons, we represent the absolute value of this potential difference with V rather than with the V we used in previous notation. The charge q and the potential difference V for a capacitor are proportional to each other; that is, q CV. (25-1) The proportionality constant C is called the capacitance of the capacitor. Its value depends only on the geometry of the plates and not on their charge or potential difference. The capacitance is a measure of how much charge must be put on the plates to produce a certain potential difference between them: The greater the capacitance, the more charge is required. The SI unit of capacitance that follows from Eq. 25-1 is the coulomb per volt. This unit occurs so often that it is given a special name, the farad (F): 1 farad 1 F 1 coulomb per volt 1 C/V. (25-2) As you will see, the farad is a very large unit. Submultiples of the farad, such as the microfarad (1 mF 106 F) and the picofarad (1 pF 1012 F), are more convenient units in practice. Charging a Capacitor One way to charge a capacitor is to place it in an electric circuit with a battery. An electric circuit is a path through which charge can flow. A battery is a device that maintains a certain potential difference between its terminals (points at which charge can enter or leave the battery) by means of internal electrochemical reactions in which electric forces can move internal charge. In Fig. 25-4a, a battery B, a switch S, an uncharged capacitor C, and interconnecting wires form a circuit. The same circuit is shown in the schematic diagram of Fig. 25-4b, in which the symbols for a battery, a switch, and a capacitor represent those devices. The battery maintains potential difference V between its terminals. The terminal of higher potential is labeled  and is often called the positive terminal; the terminal of lower potential is labeled  and is often called the negative terminal. 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 field lines show, the electric field due to the charged plates is uniform in the central region between the plates.The field is not uniform at the edges of the plates, as indicated by the “fringing” of the field lines there. Area A V d Top side of bottom plate has charge –q A –q +q (a) (b) Bottom side of top plate has charge +q Electric field lines 719 The circuit shown in Figs. 25-4a and b is said to be incomplete because switch S is open; that is, the switch does not electrically connect the wires attached to it. When the switch is closed, electrically connecting those wires, the circuit is complete and charge can then flow through the switch and the wires. As we discussed in Chapter 21, the charge that can flow through a conductor, such as a wire, is that of electrons. When the circuit of Fig. 25-4 is completed, electrons are driven through the wires by an electric field that the battery sets up in the wires. The field drives electrons from capacitor plate h to the positive terminal of the battery; thus, plate h, losing electrons, becomes positively charged. The field drives just as many electrons from the negative terminal of the battery to capacitor plate l; thus, plate l, gaining electrons, becomes negatively charged just as much as plate h, losing electrons, becomes positively 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 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 situation 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 After reading this module, you should be able to . . . 25.01 Sketch a schematic diagram of a circuit with a parallelplate 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. 25.03 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. ● A capacitor consists of two isolated conductors (the plates) with charges q and q. Its capacitance C is defined 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. Learning Objectives Key Ideas 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. Figure 25-1 An assortment of capacitors. +q –q Paul Silvermann/Fundamental Photographs 718 CHAPTER 25 CAPACITANCE Figure 25-4 (a) Battery B, switch S, and plates h and l of capacitor C, connected in a circuit. (b) A schematic diagram with the circuit elements represented by their symbols. l V + – (b) C B Terminal S (a) + – B S h l C h Terminal shape. No matter what their geometry, flat or not, we call these conductors plates. Figure 25-3a 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 difference between the two plates. For historical reasons, we represent the absolute value of this potential difference with V rather than with the V we used in previous notation. The charge q and the potential difference V for a capacitor are proportional to each other; that is, q CV. (25-1) The proportionality constant C is called the capacitance of the capacitor. Its value depends only on the geometry of the plates and not on their charge or potential difference. The capacitance is a measure of how much charge must be put on the plates to produce a certain potential difference between them: The greater the capacitance, the more charge is required. The SI unit of capacitance that follows from Eq. 25-1 is the coulomb per volt. This unit occurs so often that it is given a special name, the farad (F): 1 farad 1 F 1 coulomb per volt 1 C/V. (25-2) As you will see, the farad is a very large unit. Submultiples of the farad, such as the microfarad (1 mF 106 F) and the picofarad (1 pF 1012 F), are more convenient units in practice. Charging a Capacitor One way to charge a capacitor is to place it in an electric circuit with a battery. An electric circuit is a path through which charge can flow. A battery is a device that maintains a certain potential difference between its terminals (points at which charge can enter or leave the battery) by means of internal electrochemical reactions in which electric forces can move internal charge. In Fig. 25-4a, a battery B, a switch S, an uncharged capacitor C, and interconnecting wires form a circuit. The same circuit is shown in the schematic diagram of Fig. 25-4b, in which the symbols for a battery, a switch, and a capacitor represent those devices. The battery maintains potential difference V between its terminals. The terminal of higher potential is labeled  and is often called the positive terminal; the terminal of lower potential is labeled  and is often called the negative terminal. 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 field lines show, the electric field due to the charged plates is uniform in the central region between the plates.The field is not uniform at the edges of the plates, as indicated by the “fringing” of the field lines there. Area A V d Top side of bottom plate has charge –q A –q +q (a) (b) Bottom side of top plate has charge +q Electric field lines 719 The circuit shown in Figs. 25-4a and b is said to be incomplete because switch S is open; that is, the switch does not electrically connect the wires attached to it. When the switch is closed, electrically connecting those wires, the circuit is complete and charge can then flow through the switch and the wires. As we discussed in Chapter 21, the charge that can flow through a conductor, such as a wire, is that of electrons. When the circuit of Fig. 25-4 is completed, electrons are driven through the wires by an electric field that the battery sets up in the wires. The field drives electrons from capacitor plate h to the positive terminal of the battery; thus, plate h, losing electrons, becomes positively charged. The field drives just as many electrons from the negative terminal of the battery to capacitor plate l; thus, plate l, gaining electrons, becomes negatively charged just as much as plate h, losing electrons, becomes positively