Analogy to Electrical Circuits

The integration of Equation 8.36 between the limits of x=0 and x=L by keeping /, constant yields 

As described in Section 3.2, ion distributions near a charged interface lead to a net accumulation of one kind of ions. As a result, the two sides of the membrane can acquire a charge buildup upon imposition of electric potentials on them. The net charge Qm on the membrane built up this way is 

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With analogy to electric circuits, a transfer function of the antenna can be calculated and the response of the antenna to an incoming wave obtained. The output signal is usually expressed as antenna cross-section. It is defined as the ratio between the total energy absorbed by the antenna and the incident spectral density function of the incident wave. In the case of Nautilus antenna (2300 kg, 3 x 0.6 m) the cross-section is of the order of 10 25m2 Hz. 

The analogy to electrical circuits is also used to extend the relationships derived in section 1.2.1 for overall heat transfer, to walls with several layers. Walls with two or more layers are often used in technical practice. A good example of these multi-layer walls is the addition of an insulating layer made from a material with low thermal conductivity Ais. Fig. 1.13 shows a temperature profile for a wall that consists of a number of layers. The resistance to heat transfer for each layer in series is added together and this gives the overall heat transfer resistance for the wall as... 

A common way of approaching problems with multi-layered systems is to consider each of the layers as a resistance to heat transfer (analogous to electrical circuits). In this case, because each refractory/insulating material is layered onto the previous material, these thermal resistances can be considered as being in series and are thus additive. In heat transfer, the resistance typically has units of temperature over heat rate (such as K W ). 

Thermal equation is analogous to electrical-circuit equation. Electrical power consumption P corresponds to a current source. Static heat-transfer properties are usually specified using a thermal resistance that defines a relation between heat flow per unit time Q and temperature difference e = T-To ... 

In analogy to electrical circuits, for combining conductances, one can apply Kirchhoff s laws to calculate the total conductance, Cj, of an assembly of elements. If two parts are connected in parallel, the total conductance wiU be Cp = Q -F Cz, and if they are connected in series, it will be -F Thus, the simple consequence for the serial connection is that the smallest conductance wiU determine the conductance of the assembly. 

How does one know when the complete roster of reaction schemes that are consistent with the rate law has been obtained One method is based on an analogy between electrical circuits and reaction mechanisms.13 One constructs an electrical circuit analogous to the reaction scheme. Resistors correspond to transition states, junctions to intermediates, and terminals to reactants and products. The precepts are these (1) any other electrical circuit with the same conductance corresponds to a different but kinetically equivalent reaction scheme, and (2) these circuits correspond to all of the fundamentally different schemes. 

Equation (4) is analogous to electrical current flowing through electrical resistances in series. Figure 3 illustrates such an electrical circuit, where an electrical current, i, flows through a series of three resistances, Ri, i 2 and R3. The overall voltage difference of F0 — V3, is given by... 

III lieal iraiisler analysis, vve are often iiitetested in the rate of heat transfer through a medium under steady conditions and surface temperatures. Such problems can be solved easily without involving any differential equations by (he introduction of the iheimal resislance concept in an analogous manner to electrical circuit problems. In this case, the thennal resistance corresponds to electrical resistance, temperature difference corresponds to voltage, and the heat transfer rate coiresponds to electric current. 

The analogy with electric circuits made earlier is certainly not an obvious one. and in the works of Vorkenshtein and Gordshtein (2,3), a requirement exists that the kinetic graph for noncataly tic reactions contain a nuU vertex with a concentration equal to 1. For catalytic reactions the role of the null vertex is that of a free catalytic surface. 

Clearly, Eq. (1.79) readily admits an interpretation in terms of the electric-circuit theory as shown in Fig. 1.21, where temperatures are analogous to potentials (voltages) and heat flux is analogous to electric current. In Section 2.2 of Chapter 2 dealing with composite structures we shall again utilize this analogy. ... 

In this work, the foam board was assumed to be made up of stacked and juxtaposed cubic unit cells which can be seen in Figure 2 (a). Hence, the total thermal resistance of the foam board was a summation of thermal resistance of each cell in series. To calculate the thermal resistance of each cell, a cubic-series-parallel analogy of electric circuit [10] was applied. As shown in Figure 2 (b), this approach considered that the four side walls with the same cross-sectional area and the central gas cube which includes the borders along the cell corners were a compound material. Thus, the thermal resistance of each cell was derived. 

Previously the analogy between electric fields and magnetic fields was introduced. Likewise, there are analogies between magnetic circuits and electric circuits. Figure 2-67 illustrates these analogies and allows us to define additional terms. In the electric circuit of Figure 2-67a Ohm s law applies, i.e.. 

Edwards equation, 230-232 Electrical circuits, analogs to mechanisms, 138-139 Electron exchange, 243 Electrostatic effects, 203 Elementary reaction, 2, 4, 12, 55 rate of, 5... 

The harmonic oscillator is an important system in the study of physical phenomena in both classical and quantum mechanics. Classically, the harmonic oscillator describes the mechanical behavior of a spring and, by analogy, other phenomena such as the oscillations of charge flow in an electric circuit, the vibrations of sound-wave and light-wave generators, and oscillatory chemical reactions. The quantum-mechanical treatment of the harmonic oscillator may be applied to the vibrations of molecular bonds and has many other applications in quantum physics and held theory. 

The successive corrections necessary to transform the thermogram g(t) into f(t), according to Eqs. (33), may be done by adding to the amplification and recording line a suitable analog RC network (40, 46, 66). The electrical circuit, presented on Fig. 12, transforms any voltage function flffc—1(<) (the input) into a new function of time gk(t) (the output) which is related to gk-i(t) by... 

Current is a measure of electron flow rate in an electrical circuit, analogous to water flow rate through a pipe, and is symbolized by I. Current is measured in amperes (amps), symbolized as A miUiamperes (milliamps), symbolized as mA or microamperes (microamps), symbolized as ptA. An ampere is an electron flow of 6.23 xlO18 electrons per second passing through the circuit. 

An analogous term to voltage when considering electrical circuits and components (volts, E). 

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