Electrostatic Energy Stored in a Capacitor

The electrostatic energy, W, expressed in joules (J), stored in a capacitor is given by the following equation  

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The static permittivity or dielectric constant of a material under given conditions reflects the extent to which it concentrates electrostatic lines of flux. Technically, it is the ratio of the amount of electrical energy stored in a material by an applied voltage, relative to that stored in a vacuum. Similarly, it is also the ratio of the capacitance of a capacitor using that material as a dielectric, compared to a similar capacitor which has a vacuum as its dielectric. The dielectric constant values of water have been given, for example, by Fernandez et al. (1995). 

Theoretically, the origin of the film instability is best understood by considering the balance of forces acting at the polymer film-air interface. As discussed before, the film surface tension y minimizes the area of the polymer-air interface and stabilizes the film. The electric field on the other hand polarizes the polymer resulting in an effective surface charge density. This result in an electrostatic pressure at the liquid-air interface. An expression for p i is obtained by minimization of the energy, Tel> stored in the capacitor with a constant applied voltage, U, as [29] ... 

Following a period of charge, the capacitor will store a small amount of energy as an electrostatic charge which, we will see later, can be made to do work. The energy stored (symbol W) in a capacitor is expressed in joules and given by the formula ... 

An electrochemical capacitor differs from a conventional electrostatic capacitor in that the energy is stored in the form of ions rather than electrons. This results in an increase in the amount of energy that is stored at the expense of reduced power output per unit mass/volume. Thus, an electrochemical capacitor begins to assume some of the characteristics of a rechargeable battery. Such devices are variously referred to as supercapacitors and ultracapacitors . Since there is some confusion over the distinction, we prefer to use the generic term electrochemical capacitor . 

The association of an inductor with a capacitor allows the two snbvarieties of electrodynamical energy, inductive (electromagnetic) and capacitive (electric or electrostatic), to be stored in the same system. The two system constitutive properties, inductance and capacitance, are the supports for the storage of energy and they link the state variables according to the following relations ... 

Capacitance The property of a device or component that enables it to store energy in an electrostatic field and to release it later. A capacitor consists of two conductors separated by an insulating material. When the conductors have a voltage difference between them, a charge will be stored in the electrostatic field between the conductors. 

Capacitor A capacitor is a passive electronic component that stores energy in the form of an electrostatic field. The simplest form of capacitor consists of two conducting plates separated by an insnlating material called the dielectric. 

A classic definition of electrochemical ultracapacitors or supercapacitors summarizes them as devices, which store electrical energy via charge in the electrical double layer, mainly by electrostatic forces, without phase transformation in the electrode materials. Most commercially available capacitors consist of two high surface area carbon electrodes with graphitic or soot-like material as electrical conductivity enhancement additives. Chapter 1 of this volume contains seven papers with overview presentations, and development reports, as related to new carbon materials for this emerging segment of the energy market. 

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