Parallel resistance-capacitance measurements

To investigate the main factors in the low-temperature (LT) power decline, the impedance spectra were first determined at different temperatmes (Figure 20). In the case of the impedance spectra for the cathode, the first and second semicircles, caused by the reactions in the SEl and the interfacial charge transfer combined with double layer charging, respectively, increased in size with lowering temperature while the inclined line due to the solid-state diffusion process became shorter. From the separated semicircles in the impedance spectra for the anode measured at the low temperatures, it is proved that at least four parallel resistive-capacitive elements were needed to properly model the reactions in the anode during battery operation, the basis for which is not yet clearly understood. 

The bipolar pulse technique for measuring solution resistance minimizes the effects of both the series and parallel cell capacitances in a unique way. The instrumentation for this technique is illustrated in Figure 8.15. The technique consists of applying two consecutive voltage pulses of equal magnitude and pulse width but of opposite polarity to a cell and then measuring the cell current precisely at the end of the second pulse [18]. 

Bridge measurements provide the most direct way to compare an unknown impedance with known standard impedances. The impedance may be a pure resistance, capacitance, or inductance, or may be represented by some series or parallel combination. The DC Wheatstone bridge95 provides a simple and... 

The impedance of the skin has been generally modeled by using a parallel resistance/capacitor equivalent circuit (Fig. 4a). The skin s capacitance is mainly attributed to the dielectric properties of the lipid-protein components of the human epidermis [5,8,9,12]. The resistance is associated primarily with the skin s stratum comeum layer [5,8,9,12]. Several extensions to the basic parallel resistor/capacitor circuit model have appeared in the literature [5,8,9,13]. Most involve two modified parallel resistor/capacitor combinations connected in series [5,8,9]. The interpretation of this series combination is that the first parallel resistor/capacitor circuit represents the stratum comeum and the second resistor/capacitor parallel combination represents the deeper tissues [5,8,9]. The modification generally employed is to add another resistance, either in series and/or in parallel with the original parallel resistor/capacitor combination [8,9]. Realize that because all of these circuits contain a capacitance, they will all exhibit a decrease in impedance as the frequency is increased. This is actually what is observed in all impedance measurements of the skin [5,6,8-15]. In addition, note that the capacitance associated with the skin is 10 times less than that calculated for a biological membrane [12]. This... 

The use of a small electrolyte covered resist area around the microelectrode is essential when capacitance measurements are performed, as the resist capacitance is parallel to the electrode capacitance. With a specific resistance of a = 1012 LI cm and a dielectric constant of e = 1.5 for the resist, and assuming a typical electrode capacitance of 10pFcm 2 with a 50 tm electrode, an error of 5% is obtained, if the electrolyte covered surface is 10 3cm2 (/=1000Hz) [88]. Thus, for capacitance measurements, the use of nanoliter droplets is essential. 

The revelation that Cp is indeed a novel capacitance requires the inclusion of two capacitances in the equivalent circuit shown in Figure 2 (36, 37). In essence, with the exception of a genuine short-circuit measurement, the macroscopically measured photosignal is a manifestation of the interaction of two circuits in parallel One circuit represents the photochemical event associated with bacteriorhodopsin, and the other circuit represents the resistance-capacitance (RC) relaxation event of the inert supporting structure —the membrane dielectric. 

The apparatus used in our study of thin liquid films is shown diagrammatically in Fig. 1 [16, 17, 85, 86]. There is a hole (0.5 mm in diameter) in the side of the Teflon chamber, which separates two aqueous solutions. The oil phase containing film-forming substances is introduced into the hole with the aid of a small syringe (ATP Inc., MI, USA). The film capacitance (Cm) and resistance were measured by a Multi-Function Analyzer (Sino-Jinke Electronics Co. Ltd, Tianjin, China). The thickness of thin liquid films, according to the parallel-plate formula, is given by... 

Knowing the SC thickness enabled the authors to calculate the parallel resistivity and relative permittivity of the removed SC. Furthermore, the resistivity and relative permittivity of the viable skin was calculated by assuming homogenous electrical properties and using the formula for constrictional resistance (cf. Figure 6.3). The resistance of the disk surface electrode is (Eq. 6.17) R = p/4a. Because RC = pcj-eo, the relative permittivity of the viable skin can be calculated from the measured capacitance with a similar formula ... 

Impedance interfaces often provide the facility for automatically switching between measurements of the sample to be measured and measurements of a low loss calibrated reference capacitor (Figure 3.2.10). An ideal reference capacitor would have a completely flat response (constant capacitance) across the entire frequency range. This ideal capacitor cannot be achieved in reality since there will always be some parallel resistance in the capacitor even though this can, in practice, be an extremely high value. However, the difference between an ideal and nonideal capacitor is sufficiently small for most purposes and the reference capacitor is a very useful tool that can be used to quantify errors due to cables and instrument measurement errors. The deviation of the capacitor from its ideal response due to cables... 

The gavanostatic transient method can be used to measure the double layer capacity and the ohmic drop in the electrolyte between the working and reference electrodes. Figure 5.14 shows the initial variation of the potential resulting from a current step. During this period, diffusion is of little importance because its time constant is usually much larger. The electrode acts like a capacitor connected in parallel with a resistance, where the capacitor represents the double layer capacity and the parallel resistance corresponds to the transfer resistance of the electrode reaction (Section 3.5). The applied current I is the sum of the capacitive current Iq given by (5.94) and the faradaic current I-p described by the Butler-Volmer equation ... 

A biological material (a dielectric) can be exposed to electric or magnetic fields in frequencies from direct current (OHz) to x-rays (wlO Hz). From direct current to ac frequencies up to about 8 Hz, lumped circuits (composed of serial and parallel resistances and capacitance elements) are used to measure... 

As was previously indicated, IS measurements can also be used to determined membrane modifications and Figure 9.13 shows Nyquist and Bode plots for PS-Uf and PS-Uf/BSA fouled membranes in contact with a NaCl solution. Here a significant increase in electrical resistance due to membrane fouling can be observed, but the electrolyte contribution hardly differs in both systems. In both cases, the equivalent circuit for the membrane-electrolyte system is given by (R,C,)-(RM that is, a series association of the electrolyte part, formed by a resistance in parallel with a capacitor and the membrane part, which consists of a parallel association of a resistance and a CPE or non-ideal capacitor (RmQm). Fitting the experimental data allows determination of the electrical parameters (resistance, capacitance) for the different NaCl solutions studied and their variation with electrolyte concentration is shown in Figure 9.13c, d, respectively. 

The capacitance. The electrical double layer may be regarded as a resistance and capacitance in parallel see Section 20.1), and measurements of the electrical impedance by the imposition of an alternating potential of known frequency can provide information on the nature of a surface. Electrochemical impedance spectroscopy is now well established as a powerful technique for investigating electrochemical and corrosion systems. 

In the measurements, one commonly determines the impedance of the entire ceU, not that of an individual (working) electrode. The cell impedance (Fig. 12.13) is the series combination of impedances of the working electrode (Z g), auxiliary electrode (Z g), and electrolyte (Z ), practically equal to the electrolyte s resistance (R). Moreover, between parallel electrodes a capacitive coupling develops that represents an impedance Z parallel to the other impedance elements. The experimental conditions are selected so that Z Z g Z g. To this end the surface area of the auxiliary electrode should be much larger than that of the working electrode, and these electrodes should be sufficiently far apart. Then the measured cell impedance... 

To find the relation between the values of R and measured experimentally in terms of the circuit of Fig. 12.11a and the parameter values in the circuit of Fig. 12.14a, we must first convert [with the aid of Eq. (12.23)] the parameters of the circuit with parallel elements Ry and Q into the parameters of a circuit with a resistance and capacitance in series, and to the value of resistance obtained we must add R.. As a result, we have... 

The impedance data have been usually interpreted in terms of the Randles-type equivalent circuit, which consists of the parallel combination of the capacitance Zq of the ITIES and the faradaic impedances of the charge transfer reactions, with the solution resistance in series [15], cf. Fig. 6. While this is a convenient model in many cases, its limitations have to be always considered. First, it is necessary to justify the validity of the basic model assumption that the charging and faradaic currents are additive. Second, the conditions have to be analyzed, under which the measured impedance of the electrochemical cell can represent the impedance of the ITIES. 

Most often, the electrochemical impedance spectroscopy (EIS) measurements are undertaken with a potentiostat, which maintains the electrode at a precisely constant bias potential. A sinusoidal perturbation of 10 mV in a frequency range from 10 to 10 Hz is superimposed on the electrode, and the response is acquired by an impedance analyzer. In the case of semiconductor/electrolyte interfaces, the equivalent circuit fitting the experimental data is modeled as one and sometimes two loops involving a capacitance imaginary term in parallel with a purely ohmic resistance R. 

To understand the electrical behaviour of the LAPS-based measurement, the LAPS set-up can be represented by an electrical equivalent circuit (see Fig. 5.2). Vbias represents the voltage source to apply the dc voltage to the LAPS structure. Re is a simple presentation of the reference electrode and the electrolyte resistance followed by a interface capacitance Cinterface (this complex capacitance can be further simulated by different proposed models as they are described, e.g., in Refs. [2,21,22]). In series to the interface capacitance, the insulator capacitance Cj will summarise the capacitances of all insulating layers of the LAPS device. The electrical current due to the photogeneration of electron-hole pairs can be modelled as current source Ip in parallel to the... 

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