Resistance, circuit element representation

To discuss the results, the sensor is represented as a lossy capacitor, with both the capacitance C and the resistance R depending on frequency (Fig. 4 the frequency dependence of the equivalent-circuit elements is a consequence of the distributed nature of the processes in the sensor, which cannot be modeled appropriately by only two lumped elements with frequency-independent element values.). That simplifies the recognition of even small changes in the impedance, as changes at low frequencies become easily visible in the representation of the resistance R(f) and changes at higher frequencies become even more visible in the representation of the capacitance C(f). 

Representation of a Circuit Element by a Current Source and Resistance... 

FIGURE 1.67 Representation of circuit elements by resistance and current source, (a) Inductance, (b) Capacitance, (c) Distributed line. 

In another study of DMFC anodes, shovm in Figure 16.10, the complex-plane impedance plots were studied as a function of the current density applied. The diameters of the semicircles were found to decrease with increasing current density, as expected, but the new feature observed is an inductive branch of the curves. This can be modeled, of course, by adding an inductive element to the equivalent circuit representation, in series with the Faradaic resistance, but the physical origin of this added circuit element is still open for debate. There is a tendency to associate it with sluggish adsorption of CO, formed as an intermediate in the oxidation of methanol. However, unlike the adsorption pseudocapacitance, which is well understood (cf Section 11.2), there is no theory for the dependence of the pseudoinductance on potential, coverage or any other measured parameter. 

III.l [see also Eq. (17) and Fig. 2], and that in the presence of a faradaic reaction [Section III. 2, Fig. 4(a)] are found experimentally on liquid electrodes (e.g., mercury, amalgams, and indium-gallium). On solid electrodes, deviations from the ideal behavior are often observed. On ideally polarizable solid electrodes, the electrically equivalent model usually cannot be represented (with the exception of monocrystalline electrodes in the absence of adsorption) as a smies connection of the solution resistance and double-layer capacitance. However, on solid electrodes a frequency dispersion is observed that is, the observed impedances cannot be represented by the connection of simple R-C-L elements. The impedance of such systems may be approximated by an infinite series of parallel R-C circuits, that is, a transmission line [see Section VI, Fig. 41(b), ladder circuit]. The impedances may often be represented by an equation without simple electrical representation, through distributed elements. The Warburg impedance is an example of a distributed element. 

In Chap. 2 we saw the responses of electrical circuits containing the elements R, C, and L. Because these are linear elements, their impedance is independent of the ac amplitude used. However, in electrochemical systems, we do not have such elements we have solution-electrode interfaces, redox species, adsorption, etc. In this and the following chapters, we will learn how to express the electrochemical interfaces and reactions in terms of equations that, in particular cases, can be represented by the electrical equivalent circuits. Of comse, such circuits are only the electrical representations of physicochemical phenomena, and electrical elements such as resistance, capacitance, or inductance do not exist physically in cells. However, such a presentation is useful and helps in our understanding of the physicochemical phenomena taking place in electrochemical cells. Before presenting the case of electrochemical reactions, the case of an ideally polarizable electrode will be presented. 

A rudimentary representation for an input circuit with glass microelectrodes (using a dc amplifier) is shown in Figure 7.5. represents the series resistance of the glass micropipette. A detailed description of electrode polarization problems was presented in Chapter 4. For this discussion it is sufficient to consider only the elements shown in Figure 7.5 since any signal distortion produced by electrode polarization can be incorporated into the description of. ... 

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