Charging current, equation

But there is a current flowing out of the gate described by (Vsat- Vgs)/Rdrive. Therefore this must equal the Cgd charging current. Equating terms, we get the d(Vd)/dt. and so we get the equation forVd. 

Various theoretical and empirical models have been derived expressing either charge density or charging current in terms of flow characteristics such as pipe diameter d (m) and flow velocity v (m/s). Liquid dielectric and physical properties appear in more complex models. The application of theoretical models is often limited by the nonavailability or inaccuracy of parameters needed to solve the equations. Empirical models are adequate in most cases. For turbulent flow of nonconductive liquid through a given pipe under conditions where the residence time is long compared with the relaxation time, it is found that the volumetric charge density Qy attains a steady-state value which is directly proportional to flow velocity... 

Where this equation is applied to different nonconductive liquids in different pipes, the polarity of the generated charge may change unpredictably and the proportionality constant a may vary over about an order of magnitude depending on conditions. The charging current Iq is the product of... 

To apply these data and equations to the problem of ground resistance, the maximum anticipated current must first be estimated. For practical industrial situations, Iq varies in the range 0.01-100/rA. The upper value represents extreme cases such as microfiltration and the lower value to slow flow in pipe. Typical charging currents for tank tmck loading are of the order 1 /rA (5-3.1.1). As an example, consider a system such as a tank with a capacitance less than 1000 pF. First, consider the minimum ignition voltages in Table A-4-1.3b. From Eq. (2), f L = In the case of hydrogen the mini-... 

For a simplified case, one can obtain the rate of CL emission, =ft GI /e, where /is a function containing correction parameters of the CL detection system and that takes into account the fact that not all photons generated in the material are emitted due to optical absorption and internal reflection losses q is the radiative recombination efficiency (or internal quantum efficiency) /(, is the electron-beam current and is the electronic charge. This equation indicates that the rate of CL emission is proportional to q, and from the definition of the latter we conclude that in the observed CL intensity one cannot distii pish between radiative and nonradiative processes in a quantitative manner. One should also note that q depends on various factors, such as temperature, the presence of defects, and the... 

The charging of the double layer is responsible for the background (residual) current known as the charging current, which limits die detectability of controlled-potential techniques. Such a charging process is nonfaradaic because electrons are not transferred across the electrode-solution interface. It occurs when a potential is applied across the double layer, or when die electrode area or capacitances are changing. Note that the current is the tune derivative of die charge. Hence, when such processes occur, a residual current flows based on die differential equation... 

Now we can write the equation for the charging current, ic, during the growth of the drop as... 

It is to be expected that the equations relating electromagnetic fields and potentials to the charge current, should bear some resemblance to the Lorentz transformation. Stating that the equations for A and (j> are Lorentz invariant, means that they should have the same form for any observer, irrespective of relative velocity, as long as it s constant. This will be the case if the quantity (Ax, Ay, Az, i/c) = V is a Minkowski four-vector. Easiest would be to show that the dot product of V with another four-vector, e.g. the four-gradient, is Lorentz invariant, i.e. to show that... 

The quantity sf is a result of the normalization constraint, while, sy 1 are the Lagrange multipliers associated with the charge-current conservation defined by Equation 8.17. On the other hand, if Equation 8.18 is divided by Rk we can reexpress the corresponding equation as... 

Convolution may also be applied to ohmic drop correction in the case where a substantial double-layer charging current is present, unlike the preceding case. It suffices first to extract the Faradaic current from the total current according to equation (1.19) [obtained from equations (1.11)]... 

This section is devoted to the establishment of equations (1.12) and (1.13). In addition to the dimensionless variables used previously (Section 6.1.2), we normalize the Faradaic and double-layer charging current,... 

Plug this value for time into the equation Charge=(Current in amperes)(Time in seconds) ... 

There are two types of charging currents and condenser charges, which may be described as rapidly-forming or instantaneous polarizations, and slowly-forming or absorptive polarizations. The total polarizability of the dielectric is the sum of contributions due to several types of displacement of charge produced in the material by the applied field. The relaxation time is the time required for a polarization to form or disappear. The magnitude of the polarizability, k, of a dielectric is related to the dielectric constant e as shown by the following equation ... 

The space-charge current density in vacuo expressed by Eqs. (3) and (4) constitutes the essential part of the present extended theory. To specify the thus far undetermined velocity C, we follow the classical method of recasting Maxwell s equations into a four-dimensional representation. The divergence of Eq. (1) can, in combination with Eq. (4), be expressed in terms of a fourdimensional operator, where (j, 7 p) thus becomes a 4-vector. The potentials A and are derived from the sources j and p, which yield... 

The field equations in the vacuum are (31) and (32), and there are two possible vacuum charge current 12-vectors ... 

Equation (584) implies that the topological magnetic charge-current... 

Therefore, charge density and current density in the vacuum and in matter take the same form, [see Eqs. (732) and (733)]. This is a general result of assuming an 0(3) vacuum configuration as in Section I. Equations (736) are a form of Noether s theorem and charge/current enters the scene as the result of conservation and topology. Similarly, mass is curvature of the gravitational field. 

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