Physics
Capacitor Charge
Capacitor charge refers to the process of storing electrical energy in a capacitor by accumulating an electric charge on its plates. When a voltage is applied across the capacitor, it becomes charged as electrons accumulate on one plate and leave the other. This stored charge can then be released to power electrical devices or circuits.
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11 Key excerpts on "Capacitor Charge"
eBook - PDF- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
25.4.3 For a capacitor, apply the relationship between the potential energy, the internal volume, and the internal energy density. 25.4.4 For any electric field, apply the relationship between the potential energy density u in the field and the field’s magnitude E. 25.4.5 Explain the danger of sparks in airborne dust. Figure 25.3.4 A potential difference V 0 is applied to capacitor 1 and the charging battery is removed. Switch S is then closed so that the charge on capacitor 1 is shared with capacitor 2. S C 2 C 1 q 0 After the switch is closed, charge is transferred until the potential differences match. Additional examples, video, and practice available at WileyPLUS 771 25.4 ENERGY STORED IN AN ELECTRIC FIELD Key Ideas ● The electric potential energy U of a charged capacitor, U = q 2 ___ 2c = 1 _ 2 CV 2 , is equal to the work required to charge the capacitor. This energy can be associated with the capacitor’s electric field E → . ● Every electric field, in a capacitor or from any other source, has an associated stored energy. In vacuum, the energy density u (potential energy per unit volume) in a field of magnitude E is u = 1 _ 2 ε 0 E 2 . Energy Stored in an Electric Field Work must be done by an external agent to charge a capacitor. We can imagine doing the work ourselves by transferring electrons from one plate to the other, one by one. As the charges build, so does the electric field between the plates, which opposes the continued transfer. So, greater amounts of work are required. Actually, a battery does all this for us, at the expense of its stored chemical energy. We visual- ize the work as being stored as electric potential energy in the electric field between the plates. Suppose that, at a given instant, a charge q′ has been transferred from one plate of a capacitor to the other. The potential difference V′ between the plates at that instant will be q′/C.
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 - ePubElectrochemical Supercapacitors for Energy Storage and Delivery
Fundamentals and Applications
- Aiping Yu, Victor Chabot, Jiujun Zhang(Authors)
- 2017(Publication Date)
- CRC Press(Publisher)
Figure 1.1a . This structural change was very important after both world wars when demands for electronic parts increased. Capacitors were used in complex electronic systems, resulting in greater production and standardization programs to ensure the reliability and quality of the capacitors. Significant effort to meet quality and reliability requirements contributed to the successful improvements of modern electronics. Smaller and lighter capacitors possess greater capabilities and stability in adverse conditions and over wide temperature ranges.FIGURE 1.1(See color insert.) (a) Simplified schematic of capacitor design. (b) Cross-sectional schematic of Leyden jar (water-filled glass jar containing metal foil electrodes on its inner and outer surfaces, (denoted A and B).This chapter reviews the fundamentals of capacitors and emphasizes the critical parameters of dielectric materials and the construction of capacitors, as well as their operations in a variety of applications [1 ].1.2 Electric Charge, Electric Field, and Electric Potential and Their Implications for Capacitor Cell Voltage
1.2.1 Electric Charge
The roles of a capacitor are to separate, store, and deliver electric charges and the concepts and properties of charges must be understood. In general, both positive and negative electric charges exist in all physical objects in the universe whether they are animate or inanimate. A physical object will display a neutral charge when there are equal numbers of positive charges (protons) and negative charges (electrons). However, a net electric charge can occur through unbalancing the charge equilibrium in some areas of an object. Thus some areas will have more negative than positive charges and vice versa.In general, two positive charges reciprocally repel each other as do two negative charges; while opposite charges feel mutual attractive forces. Figure 1.2
- Jerry D. Wilson, Anthony J. Buffa, Bo Lou(Authors)
- 2022(Publication Date)
- CRC Press(Publisher)
Although the symbol for a capacitor is similar, its lines are of equal length. 428 College Physics Essentials discussed until Chapter 17 , all you need to know now is that a battery removes electrons from the positive plate and transfers, or “pumps,” them through a wire to the negative plate. (Take note of Figure 16.18b – our first electric circuit diagram – for future reference.) In the process of doing work, the battery loses some of its stored chemical energy. Of primary interest here is the result: a separation of charge and the creation of an electric field between the plates of the capacitor. The battery will continue to transfer charge until the potential difference between the plates is the same as the terminal voltage of the bat- tery. When the capacitor is disconnected from the battery, the energy remains stored on it until the charge is removed. Let us use Q be the magnitude of the charge on either plate (of course the net charge on the capacitor is zero). For a capacitor, Q is proportional to the voltage (electric potential difference) applied the plates, or Q ∝ ΔV . This proportionality can be made into an equation by using a constant, C, called capacitance: Q C V C Q V = ⋅ = Δ Δ or (definition of capacitance) (16.9) SI unit of capacitance is the coulomb per volt (C/V) or the farad (F) The coulomb per volt is named the farad after Michael Faraday, a famous physicist of the nineteenth century, thus 1 C/V = 1 F. The farad is a large unit (see Example 16.6), so the microfarad (1 μF = 10 −6 F), the nanofarad (1 nF = 10 −9 F), and the picofarad (1 pF = 10 −12 F) are commonly used. 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.
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
Chapter 8 | Capacitance 361 Figure 8.15 The capacitors on the circuit board for an electronic device follow a labeling convention that identifies each one with a code that begins with the letter “C.” The energy U C stored in a capacitor is electrostatic potential energy and is thus related to the charge Q and voltage V between the capacitor plates. A charged capacitor stores energy in the electrical field between its plates. As the capacitor is being charged, the electrical field builds up. When a charged capacitor is disconnected from a battery, its energy remains in the field in the space between its plates. To gain insight into how this energy may be expressed (in terms of Q and V), consider a charged, empty, parallel-plate capacitor; that is, a capacitor without a dielectric but with a vacuum between its plates. The space between its plates has a volume Ad, and it is filled with a uniform electrostatic field E. The total energy U C of the capacitor is contained within this space. The energy density u E in this space is simply U C divided by the volume Ad. If we know the energy density, the energy can be found as U C = u E ( Ad) . We will learn in Electromagnetic Waves (after completing the study of Maxwell’s equations) that the energy density u E in a region of free space occupied by an electrical field E depends only on the magnitude of the field and is (8.9) u E = 1 2 ε 0 E 2 . If we multiply the energy density by the volume between the plates, we obtain the amount of energy stored between the plates of a parallel-plate capacitor: U C = u E ( Ad) = 1 2 ε 0 E 2 Ad = 1 2 ε 0 V 2 d 2 Ad = 1 2 V 2 ε 0 A d = 1 2 V 2 C . In this derivation, we used the fact that the electrical field between the plates is uniform so that E = V /d and C = ε 0 A/d. Because C = Q/V , we can express this result in other equivalent forms: (8.10) U C = 1 2 V 2 C = 1 2 Q 2 C = 1 2 QV .
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
Electric potential is a scalar quantity, so the total electric potential due to a collection of charges is simply the algebraic sum of the electric potentials due to the individual charges. 19.4 Capacitors A capacitor is a circuit element that consists of two conducting plates that are wired together so that each plate carries an equal magnitude Q of charge, but with opposite sign. The magnitude V of the potential difference between the plates is related to the charge by = Q CV , where C is the capacitance, which is measured in units of farads (F), where = 1 F 1 C V / . A parallel-plate capacitor consists of two flat conducting plates separated by a small distance. If the plates are separated by a distance d and the area of each plate is A, then the capacitance of a parallel-plate capacitor is given by ε = C A d 0 / (Equation 19.4.2), where ε = × ⋅ − 8.85 10 C N m 0 12 2 2 / is the permittivity of free space (Appendix A). A dielectric is an insulating material that can be polarized by an electric field. A die- lectric is characterized by its dielectric constant κ (Table 19.4.1), which is a dimensionless quantity that is a measure of the amount of polarization for a given electric field. If a die- lectric fills the space between the plates of a parallel-plate capacitor, then the capacitance is given by κε = C A d 0 / (Equation 19.4.4). The potential energy U stored in a capacitor whose capacitance is C is given by = = = U QV Q C CV 2 2 2 2 2 (19.4.5) where Q is the magnitude of the charge on either plate and V is the potential difference between the plates.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
Questions 743 Capacitor; Capacitance A capacitor consists of two isolated conductors (the plates) with charges +q and –q. Its capacitance C is defined from q = CV, (25.1.1) where V is the potential difference between the plates. Determining Capacitance We generally determine the capacitance of a particular capacitor configuration by (1) assum- ing a charge q to have been placed on the plates, (2) finding the electric field E → due to this charge, (3) evaluating the potential difference V, and (4) calculating C from Eq. 25.1.1. Some specific results are the following: A parallel-plate capacitor with flat parallel plates of area A and spacing d has capacitance C = ε 0 A ____ d . (25.2.7) A cylindrical capacitor (two long coaxial cylinders) of length L and radii a and b has capacitance C = 2πε 0 L _______ ln (b/a) . (25.2.12) A spherical capacitor with concentric spherical plates of radii a and b has capacitance C = 4πε 0 ab _____ b − a . (25.2.15) An isolated sphere of radius R has capacitance C = 4πε 0 R. (25.2.16) Capacitors in Parallel and in Series The equivalent capacitances C eq of combinations of individual capacitors con- nected in parallel and in series can be found from C eq = ∑ j=1 n C j (n capacitors in parallel) (25.3.1) and 1 ____ C eq = ∑ j=1 n 1 __ C j (n capacitors in series). (25.3.2) REVIEW & SUMMARY Equivalent capacitances can be used to calculate the capaci- tances of more complicated series–parallel combinations. Potential Energy and Energy Density The electric potential energy U of a charged capacitor, U = q 2 ___ 2C = 1 _ 2 CV 2 , (25.4.1, 25.4.2) is equal to the work required to charge the capacitor. This energy can be associated with the capacitor’s electric field E → . By extension we can associate stored energy with any electric field. In vacuum, the energy density u, or potential energy per unit volume, within an electric field of magnitude E is given by u = 1 _ 2 ε 0 E 2 .
eBook - ePubCollege Physics Essentials, Eighth Edition
Electricity and Magnetism, Optics, Modern Physics (Volume Two)
- Jerry D. Wilson, Anthony J. Buffa, Bo Lou(Authors)
- 2019(Publication Date)
- CRC Press(Publisher)
its lines are of equal length .The work to charge parallel plates occurs quickly (usually in a few microseconds) by a battery. Although batteries won’t be discussed until Chapter 17 , all you need to know now is that a battery removes electrons from the positive plate and transfers, or “pumps,” them through a wire to the negative plate. (Take note of Figure 16.18b – our first electric circuit diagram – for future reference.) In the process of doing work, the battery loses some of its stored chemical energy. Of primary interest here is the result: a separation of charge and the creation of an electric field between the plates of the capacitor. The battery will continue to transfer charge until the potential difference between the plates is the same as the terminal voltage of the battery. When the capacitor is disconnected from the battery, the energy remains stored on it until the charge is removed.Let us use Q be the magnitude of the charge on either plate (of course the net charge on the capacitor is zero). For a capacitor, Q is proportional to the voltage (electric potential difference) applied the plates, or Q ∝ Δ V . This proportionality can be made into an equation by using a constant, C , called capacitance :
SI unit of capacitance is the coulomb per volt (C/V) or the farad (F)Q = C ⋅ Δ V or C =QΔ V(definition ofcapacitance)(16.9) The coulomb per volt is named the farad after Michael Faraday, a famous physicist of the nineteenth century, thus 1 C/V = 1 F. The farad is a large unit (see Example 16.6), so the microfarad (1 µ F = 10− 6 F), the nanofarad (1 nF = 10− 9 F), and the picofarad (1 pF = 10− 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)
The first electron is easy to transfer because the plates are initially neutral, but thereafter, the work required of us progressively increases. 1. The charges on the plates increase. 2. The electric potential V between the plates increases. 3. The magnitude of the electric field E in the volume between the plates increases. 4. The electric force F opposing each additional transfer increases. 5. The work W required of us for each additional transfer increases. When we finally stop, we say that all our work W is then stored as an electric potential energy U in the capacitor. We can also say that the potential energy is stored in the electric field that we have set up in the volume between the plates. Our work went to producing that field in that volume. Of course, we cannot ourselves transfer the electrons but a battery can do the work for us. In charging a capacitor, the battery transfers some of its stored chemical energy to the energy of the electric field in the volume inside the capacitor. Let’s relate the final charge q to the stored electric potential energy U by transferring a charge increment dq ′ when the charge already on the plates is q ′ and the potential difference is already V ′ . That is the incremental work required for that particular transfer, when the capacitor happens to have charge q ′ and potential difference V ′ . To find the total work W required to reach the final charge q, we must sum all the incremental works, which increases as the existing charge q ′ increases. We sum by integration: W = ∫ dW = ∫ q 0 q ′ C dq ′ = 1 C ∫ q 0 q ′ dq ′ = 1 2C [ ( q ′ ) 2 ] q 0 = 1 2C [ q 2 − 0 ] = q 2 2C . (25.29) That work is stored as electrical potential energy and thus U = q 2 2C . (25.30) Using our basic capacitor equation, q = CV, we can also write U = (CV) 2 2C , Pdf_Folio:560 560 Fundamentals of physics and then U = 1 2 CV 2 . (25.31) These two equations for a capacitor’s potential energy hold no matter what the geometry of the capacitor is.
eBook - ePub- Gerard M Crawley(Author)
- 2017(Publication Date)
- WSPC(Publisher)
Chapter 5
Capacitive Energy Storage
Wentian Gu* , Lu Wei* ,†and Gleb Yushin* ,‡* School of Materials Science and EngineeringGeorgia Institute of TechnologyRoom 288, 771 Ferst Drive NWAtlanta, GA 30332-0245, USA† School of Materials Science and EngineeringHuazhong University of Science and TechnologyWuhan, Hubei 430074, China‡ [email protected]Capacitors are electrical devices for electrostatic energy storage. There are several types of capacitors developed and available commercially. Conventional dielectric and electrolytic capacitors store charge on parallel conductive plates with a relatively low surface area, and therefore, deliver limited capacitance. However, they can be operated at high voltages. As an alternative, electrochemical capacitors (ECs) (also called supercapacitors) store charge in electric double layers or at surface reduction–oxidation (Faradaic) sites. Thanks to the large surface area of the electrode and the nanoscale charge separation, electrochemical capacitors provide much higher capacitance, filling in the gap in the energy and power characteristics between batteries and conventional capacitors. However, they offer a lower energy density than batteries and commonly lower power than traditional capacitors. In the past decade, intensive research on ECs brought about the discovery of new electrode materials and in-depth understanding of ion behavior in small pores, as well as the design of new hybrid systems combining Faradaic and capacitive electrodes, which are essential for the enhancement of the performance of ECs.This chapter presents the classification, construction, performance, advantages, and limitations of capacitors as electrical energy storage devices. The materials for various types of capacitors and their current and future applications are also discussed.1Introduction
Capacitors are passive electrical devices which store electrostatic energy in an electric field. The basic form of a capacitor (previously called a “condenser”) consists of two parallel conductors separated by a dielectric. The ability to store charge can be characterized by a single quantity, the capacitance, with the unit Farad (F), which is defined as the ratio of the charge on one of the conductors divided by the voltage applied across the dielectric that induces this charge.
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