Physics
Parallel Plate Capacitor
A parallel plate capacitor is a simple device used to store electrical energy. It consists of two parallel conducting plates separated by a dielectric material. When a voltage is applied across the plates, an electric field is created between them, leading to the storage of electric charge. The capacitance of the capacitor depends on the area of the plates and the distance between them.
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12 Key excerpts on "Parallel Plate Capacitor"
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
(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. (You will learn more about dielectrics in the sections on dielectrics later in this chapter.) The amount of storage in a capacitor is determined by a property called capacitance, which you will learn more about a bit later in this section. Capacitors have applications ranging from filtering static from radio reception to energy storage in heart defibrillators. Typically, commercial capacitors have two conducting parts close to one another but not touching, such as those in Figure 8.2. Most of the time, a dielectric is used between the two plates. When battery terminals are connected to an initially uncharged capacitor, the battery potential moves a small amount of charge of magnitude Q from the positive plate to the negative plate. The capacitor remains neutral overall, but with charges +Q and −Q residing on opposite plates. Figure 8.2 Both capacitors shown here were initially uncharged before being connected to a battery. They now have charges of +Q and −Q (respectively) on their plates. (a) A parallel-plate capacitor consists of two plates of opposite charge with area A separated by distance d. (b) A rolled capacitor has a dielectric material between its two conducting sheets (plates). A system composed of two identical parallel-conducting plates separated by a distance is called a parallel-plate capacitor (Figure 8.3). 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.
eBook - PDF- Thomas F. Fuller, John N. Harb(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
This introduction will provide a foundation for our discussion of EDLCs, and will help to highlight the differences in physics that determine the basic operation of these capacitors. 11.1 CAPACITOR INTRODUCTION A conventional electrostatic capacitor consists of two conductors separated by a dielectric (electronic insulator). Energy storage is accomplished by charge separation, with positive charge accumulated on one conductor and nega- tive on the other (see Figure 11.1a). The charge, Q, is the amount of charge on either conductor (not the sum of the two). Capacitance is defined as the charge divided by the potential difference and relates the amount of charge stored to the electrical potential required to store that charge. C Q V (11.1) The unit for capacitance is the farad, [F], which is equiv- alent to coulomb per volt [C V 1 ]. Alternatively, we can express a differential capacitance as C d dQ dV (11.2) This differential representation of the capacitance provides additional information and is required in situations where the capacitance, C, varies with the amount of charge. In contrast, Equation 11.1 defines the integral capacitance. Figure 11.1a shows a conventional Parallel Plate Capacitor consisting of two conductive plates separated by an insulator. If the gap between the plates is a vacuum, the capacitance is constant and equal to C ε 0 A d (11.3) where d is the distance between the plates, ε 0 is the permittivity of free space, 8.8542 × 10 12 [F m 1 ], and A is the area of the plates. The electrical symbol for this capacitor is also shown in the figure. The positively charged plate is called the anode and the negatively charged plate the cathode. If the vacuum is replaced by a dielectric material, the capacitance is proportional to the 251 Electrochemical Engineering, First Edition. Thomas F. Fuller and John N. Harb. 2018 Thomas F. Fuller and John N.
eBook - ePub- Ling Bing Kong(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
2Basic Concepts of Supercapacitors
Ling Bing Kong ,1,* Wenxiu Que ,2 Lang Liu ,3 Freddy Yin Chiang Boey ,1,a Zhichuan J. Xu ,1,b Kun Zhou ,4 Sean Li, 5 Tianshu Zhang 6 and Chuanhu Wang 7Brief Introduction
This chapter aims to provide a general description on the fundamental aspects regarding supercapacitors (capacitors), which are important when developing new nanomaterials for such applications.General Descriptions of Capacitors
An electric capacitor usually consists of two conductive plates, known as electrode and made of metals, between which a piece of dielectric material is inserted as shown in Fig. 2.1 [1 ]. Dielectrics that can used to construct a capacitor include air (vacuum), oiled paper, mica, glass, porcelain and various titanates. As an external voltage is applied across the two electrodes, the charging process occurs, during which, positive charges are accumulated on the positive electrode, whereas negative charges are accumulated on the negative electrode. After the external voltage is removed, both the positive and negative charges are still at the electrodes. Therefore, the capacitor separates the electrical charges. Once the two electrodes are connected with a conductive wire, the discharging process takes place, during which the positive and negative charges will be combined through the conductive wire. As a result, the capacitor can be used to store and deliver the charges.Fig. 2.1. Schematic diagram of a parallel-plate capacitor with dielectric materials to be inserted.Capacitor voltage
Electric charge
The functions of a capacitor include separation, storage and delivering of charges. It is well known that all physical objects contain both positive and negative charges. However, a physical object is generally at a neutral state, due to the same number of positive charges and negative charges. Once a net charge is present in some areas of an object because of the unbalanced charge equilibrium, some areas will have charges that have the same quantity but opposite signs.
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- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
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 ΔV 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.
eBook - ePub- Gerard M Crawley(Author)
- 2017(Publication Date)
- WSPC(Publisher)
Fig. 2.Schematic of a dielectric capacitor.2Dielectric Capacitors
A dielectric capacitor typically consists of two conductors (parallel plates) separated by a dielectric material (dielectric), as shown in Fig. 2 . When a potential difference (voltage) is applied across the conductors, a static electric field develops across the dielectric, which induces a flow of electrons from the side of higher potential to the power source, and from the power source to the opposite side. As a result, an electron deficiency develops on one side, which becomes positively charged and an electron surplus develops at the opposite side, which becomes negatively charged. This electron flow continues until the potential difference between the two sides is equal to the applied voltage. Energy is stored in the electrostatic field.The basic equation for the capacitance of such a device is:where C is the capacitance, ε is the permittivity of the dielectric, S is the surface area of the electrode and d is the thickness of the dielectric.6Dielectric capacitors yield capacitance in the range of 0.1–1 μF with a voltage range of 50–400 V. Various dielectric materials have been adopted for such capacitors, including but not limited to paper, paraffin, polyethylene, insulated mineral oil, polystyrene, ebonite, polyethylene tetraphtharate, sulfur, mica, mylar, steatite porcelain, Al porcelain, plastics (polymers), and glass.1 Table 3
eBook - ePubElectrochemical Supercapacitors for Energy Storage and Delivery
Fundamentals and Applications
- Aiping Yu, Victor Chabot, Jiujun Zhang(Authors)
- 2017(Publication Date)
- CRC Press(Publisher)
1Fundamentals of Electric Capacitors—————1.1 Introduction
An electric capacitor has a sandwich structure containing two conductive plates (normally made of metal) surrounding a dielectric or insulator as shown in Figure 1.1a . Common dielectrics include air, oiled paper, mica, glass, porcelain, or titanate. An external voltage difference is applied across the two plates, creating a charging process. During charging, the positive charges gradually accumulate on one plate (positive electrode) while the negative charges accumulate on the other plate (negative electrode). When the external voltage difference is removed, both the positive and negative charges remain at their corresponding electrodes. In this way, the capacitor plays a role in separating electrical charges. The voltage difference between the two electrodes is called the cell voltage of the capacitor. If these electrodes are connected using a conductive wire with or without a load, a discharging process occurs—the positive and negative charges will gradually combine through the wire. In this way, the capacitor plays a role for charge storage and delivery. Before we start a deeper discussion about capacitors, explanations of their history and some fundamental concepts may be useful.1.1.1 History
Thales of Miletus, a philosopher, discovered electric charges when he rubbed amber with a cloth and observed magnetic particle attraction. Since then, the act of rubbing two non-conducting materials together to induce a charge has been treated as a demonstration of the triboelectric effect. In 1745, a better understanding of electrostatics and electrochemistry led to the invention of a condenser, as shown in Figure 1.1b
- 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)
Determining capacitance We generally determine the capacitance of a particular capacitor configuration by (1) assuming 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 equation 25.1. Some specific results are the following. A parallel-plate capacitor with flat parallel plates of area A and spacing d has capacitance C = 0 A d . (25.12) A cylindrical capacitor (two long coaxial cylinders) of length L and radii a and b has capacitance C = 2 0 L ln (b∕a) . (25.17) A spherical capacitor with concentric spherical plates of radii a and b has capacitance C = 4 0 ab b − a . (25.21) An isolated sphere of radius R has capacitance C = 4 0 R. (25.23) Capacitors in parallel and in series The equivalent capacitances C eq of combinations of individual capacitors connected in parallel and in series can be found from C eq = n ∑ j=1 C j (n capacitors in parallel) , (25.26) and 1 C eq = n ∑ j=1 1 C j (n capacitors in series) . (25.28) Equivalent capacitances can be used to calculate the capacitances 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 , (25.30, 25.31) 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 0 E 2 . (25.33) Capacitance with a dielectric If the space between the plates of a capacitor is completely filled with a dielectric material, the capaci- tance C is increased by a factor , called the dielectric constant, which is characteristic of the material.
eBook - PDF- Mike Tooley, Lloyd Dingle(Authors)
- 2010(Publication Date)
- Routledge(Publisher)
Typical materials used for dielectrics are polyester and polystyrene films and ceramic materials occurs. Table 6.7 shows values of relative permittivity and dielectric strength for some common dielectric materials. Capacitors A capacitor is a device for storing electric charge. In effect, it is a reservoir into which charge can be deposited and then later extracted. Typical applications include reservoir and smoothing capacitors for use in power supplies, coupling AC signals between the stages of amplifiers, and decoupling supply rails (i.e. effectively grounding the supply rails as far as AC signals are concerned). A capacitor can consist of nothing more than two parallel metal plates as shown earlier in Figure 6.59. To understand what happens when a capacitor is being charged and discharged take a look at Figure 6.60. If the switch is left open (position A), no charge will appear on the plates and in this condition there will be no electric field in the space between the plates nor will there be any charge stored in the capacitor. When the switch is moved to position B, electrons will be attracted from the positive plate to the positive terminal of the battery. At the same time, a similar number of electrons will move from the negative terminal of the battery to the negative plate. This sudden movement of electrons will manifest itself in a momentary surge of current (conventional current will flow from the positive terminal of the battery towards the positive terminal of the capacitor). Eventually, enough electrons will have moved to make the e.m.f. between the plates the same as that of the battery. In this state, the capacitor is said to be fully charged and an electric field will be present in the space between the two plates.
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.
- John Bird(Author)
- 2013(Publication Date)
- Butterworth-Heinemann(Publisher)
This oxide layer is very thin and forms the dielectric. (The absorbent paper between the plates is a conductor and does not act as a dielectric.) Such capacitors must always be used on d.c. and must be connected with the correct polarity; if this is not done the capacitor will be destroyed since the oxide layer will be destroyed. Electrolytic capacitors are manufactured with working voltage from 6 V to 500 V, although accuracy is generally not very high. These capacitors possess a much larger capacitance than other types of capacitors of similar dimensions due to the oxide film being only a few microns thick. The fact that they can be used only on d.c. supplies limits their usefulness. 6.12 Discharging capacitors When a capacitor has been disconnected from the supply it may still be charged and it may retain this charge for some considerable time. Thus precau-tions must be taken to ensure that the capacitor is automatically discharged after the supply is switched off. This is done by connecting a high value resistor across the capacitor terminals. 6.13 Multi-choice Questions on capacitors ana capacitance (Answers on page 283.) 1. Electrostatics is a branch of electricity concerned with (a) energy flowing across a gap between conductors; (b) charges at rest; (c) charges in motion; (d) energy in the form of charges. 2. The capacitance of a capacitor is the ratio (a) charge to p.d. between plates; (b) p.d. between plates to plate spacing; (c) p.d. between plates to thickness of dielec-tric; (d) p.d. between plates to charge. 3. The p.d. across a 10 capacitor to charge it with 10 mC is (a) 100 V; (b) 1 kV; (c) 1 V; (d) 10 V. 4. The charge on a 10 pF capacitor when the voltage applied to it is 10 kV is (a) 100 μθ, (b) 0.1 C; (c) 0.1 μθ, (d) 0.01 5. Four 2 μ¥ capacitors are connected in paral-lel. The equivalent capacitance is (a) 8 ; (b) 0.5 6. Four 2 μ¥ capacitors are connected in series. The equivalent capacitance is: (a) 8 μ¥; (b) 0.5 7.
eBook - ePubSupercapacitors and Their Applications
Fundamentals, Current Trends, and Future Perspectives
- Anjali Paravannoor, Baiju K.V., Anjali Paravannoor, Baiju K.V.(Authors)
- 2023(Publication Date)
- CRC Press(Publisher)
6 ]:C =Adε 0ε r(2.1) so that a high surface area electrode would provide an extraordinary capacitance value. At the same time, this electrostatic mechanism would allow the device a quick response which in turn would improve the power profile with a power density as high as 15 kW/kg on average and a very long lifespan in the order of 1,000,000 cycles.2.2 Electrical Double-Layer Theories
When a charged object (electrode) is in contact with a liquid (electrolyte), a layer of opposite charges from the liquid concentrates near the surface of the object to balance the charge on it, to form an electrical double layer at the interface separating the electrode and the electrolyte. The formation of such a layer at the interface and the subsequent interaction between the electrode surface and electrolyte ions are explained by many different models and theories. Three prominent models are given below.2.2.1 The Helmholtz Model
Hermann von Helmholtz proposed that when an electrode is in contact with an electrolyte, ions of opposite charge tend to attract while ions of same charge repel.This results in the formation of two layers at the electrode/electrolyte interface and is called an electrical double layer. This electrical double layer can be considered as a molecular dielectric that can store an electric charge. The value of capacity for this molecular dielectric can be written as:C =Aε 0ε rX H(2.2) where X H is the ionic radius (distance of closest approach of the charges),is the relative permittivity (dielectric constant), ε0 is the permittivity of vacuum and A is the surface area accessible to the electrolyte ions. The value of capacity does not vary with applied potential the potential falls linearly from φ M to φ S where φ M is the value of electrostatic potential in the metal electrode and φ S its value in the solution (Figure 2.1(a) ). This is the simplest approach to interpret a double layer. But this model does not consider diffusion of ions, adsorption of ions at the surface of the electrode and the interaction between dipole moments of the electrode and the solvent [7 , 8ε r
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