Series a.c. circuits

An a.c. series circuit has an inductive reactance of 4 n and a resistance of 3n. The impedance of this circuit will be ... 

Ia early telephoaes, souad (voice) waves caused a carboa microphone s resistance to vary, thus varyiag the current flowing ia a series external circuit. This d-c curreat could thea be used to regeaerate voice waves ia a receiver. Two wires were required to carry a single coaversatioa. With time, telecommunications traffic was eacoded oa a-c carriers, at first usiag ampHtude or frequeacy modulatioa, and more recently pulse code modulation. 

These are unidirectional and uncontrollablet static electronic devices and used as static switches and shown in Figure 6.14. A diode turns ON at the instant it becomes forward biased and OFF when it becomes reverse biased. By connecting them in series parallel combinations, they can be made suitable for any desired voltage and current ratings. Whether it is a transistor scheme or a thyristor scheme, they are used extensively where a forward conduction alone is necessary and the scheme calls for only a simple switching, without any control over the switching operation. They are used extensively in a rectifier circuit to convert a fixed a.c. supply to a fixed d.c. supply. 

Buzsaki, G., Geisler, C., Henze, D. A. and Wang, X. J. Interneuron diversity series circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci. 27 186-193,2004. 

An alternative way of measurement is to incorporate the cell in a bridge circuit as shown in Fig. 16. The configuration of the bridge is identical to the classical Wien bridge [49] except that the a.c. voltage is supplied via the potentiostat so that, simultaneously, the mean d.c. potential E can be controlled as usual [21, 22]. The adjustable series combination of the resistor Rs and the capacitor Cs offers an impedance Zs, given by... 

Figure 5.1 Schematic representation of an electrochemical cell (a) three electrodes (b) equivalent circuit for three-electrode cell (c) equivalent circuit for the working-electrode interphase (d) a solution impedance in series with two parallel surface impedances.

In order to assess the effect of Cp on the conductance measurements, the analysis of the parallel RC network of Figure 8.9a may be carried out in a manner analogous to the series network discussed previously. The situation differs from the series circuit in that in this case, the voltage is the same across R and C, and the currents ic and iR in Cp and R are different. The instantaneous currents are given by... 

Figure 25.2 Constant-current source using a battery and series resistor, (a) Dummy (resistor) load (b) Norton s equivalent circuit for part a (c) electrolysis cell as the load.

Figure 6.24 (a) Electrical equivalent circuit for a conductance cell (b) AC bridge with the cell impedance balanced by a series R-C combination (c) AC bridge with the cell impedance balanced by a parallel R-C combination (see Table 6.7). 

There is an equivalence between the differential equations describing a mechanical system which oscillates with damped simple harmonic motion and driven by a sinusoidal force, and the series L, C, R arm of the circuit driven by a sinusoidal e.m.f. The inductance Li is equivalent to the mass (inertia) of the mechanical system, the capacitance C to the mechanical stiffness and the resistance Ri accounts for the energy losses Cc is the electrical capacitance of the specimen. Fig. 6.3(b) is the equivalent series circuit representing the impedance of the parallel circuit. 

A major use of high-quality pot-core inductors is in combination with capacitors in filter circuits. They were once extensively used in telephone systems but solid state switched systems have replaced them. The soft MnZn and NiZn ferrite systems are dominant for pot-core manufacture, although metal dust cores are used for certain applications. The important design principles can be understood by reference to a simple series LCR circuit to which a sinusoidal voltage U of angular frequency co is applied (Fig. 9.46). The circuit impedance Z = R+](coL - 1/coC) is a minimum when ojZ, = /<<>C. Thus the resonant frequency o0 is given by... 

Based on these equations, a graphical representation of the AC impedance of the (R-C-L) circuit is given in Figure 2.25. As shown in the complex plane of this figure, the AC impedance of the series RCL circuit is a straight line with a constant Z value of R. 

The a.c. impedance technique [33,34] is used to study the response of the specimen electrode to perturbations in potential. Electrochemical processes occur at finite rates and may thus be out of phase with the oscillating voltage. The frequency response of the electrode may then be represented by an equivalent electrical circuit consisting of capacitances, resistances, and inductors arranged in series and parallel. A simplified circuit is shown in Fig. 16 together with a Nyquist plot which expresses the impedance of the system as a vector quantity. The pattern of such plots indicates the type and magnitude of the components in the equivalent electrical network [35]. 

A schematic of the apparatus is shown in Figure 2. The series resistor senses current. When the overall circuit RC (R and C are circuit resistance and capacitance, respectively) time constant is short compared with the voltage developed on the sensing resistor is proportional to the instantaneous... 

The antenna consists of a resonant if circuit with parallel and series capacitors, Cp and Cs, for tuning of the resonance frequency and for matching of the impedance, respectively (Fig. 2.3.5(a)). The impedance is a complex quantity which needs to be adjusted to 50 Q magnitude and 0° phase for optimum transfer of rf power. Depending on the equivalent resistance R, inductance L, and capacitance C of the components of the antenna (Fig. 2.3.5(b)), the quality factor... 

Experiments carried out on monocrystalline Au(lll) and Au(lOO) electrodes in the absence of specific adsorption did not show any fre-quency dispersion. Dispersion was observed, however, in the presence of specific adsorption of halide ions. It was attributed to slow adsorption and diffusion of these ions and phase transitions (reconstructions). In their analysis these authors expressed the electrode impedance as = R, + (jco iJ- where is a complex electrode capacitance. In the case of a simple CPE circuit, this parameter is = T(Jcaif. However, an analysis of the ac impedance spectra in the presence of specific adsorption revealed that the complex plane capacitance plots (C t vs. Cjnt) show the formation of deformed semicircles. Consequently, Pajkossy et al. proposed the electrical equivalent model shown in Fig. 29, in which instead of the CPE there is a double-layer capacitance in parallel with a series connection of the adsorption resistance and capacitance, / ad and Cad, and the semi-infinite Warburg impedance coimected with the diffusion of the adsorbing species. A comparison of the measured and calculated capacitances (using the model in Fig. 29) for Au(lll) in 0.1 M HCIO4 in ths presence of 0.15 mM NaBr is shown in Fig. 30. 

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