Circuit elements inductances

In the parallel configuration, the same potential difference occurs across each and every element with the total current being the algebraic sum of the current flowing through each individual circuit element. Table 2-35 summarizes the equivalent resistance, conductance, capacitance, and inductance of series-parallel configurations of resistors, capacitors, and inductors. 

Strictly, the strain gauges referred to above come into this category, since in such cases the change in the measured quantity causes a corresponding change in the resistance of the element. However, the principle has a much wider application, using changes in either the inductive or capacitive reactance of electrical circuit elements. 

The mathematical expressions which describe the impedance of some passive circuits are shown below, where a passive circuit is one that does not generate current or potential [129], In this regard, the impedance response of simple passive circuit elements, such as a pure resistor with resistance R, a pure capacitor with capacitance C, and a pure inductor with inductance L, are given, respectively ... 

EIS data analysis is commonly carried out by fitting it to an equivalent electric circuit model. An equivalent circuit model is a combination of resistances, capacitances, and/or inductances, as well as a few specialized electrochemical elements (such as Warburg diffusion elements and constant phase elements), which produces the same response as the electrochemical system does when the same excitation signal is imposed. Equivalent circuit models can be partially or completely empirical. In the model, each circuit component comes from a physical process in the electrochemical cell and has a characteristic impedance behaviour. The shape of the model s impedance spectrum is controlled by the style of electrical elements in the model and the interconnections between them (series or parallel combinations). The size of each feature in the spectrum is controlled by the circuit elements parameters. 

In the vicinity of resonances, the somewhat complicated algebraic form of the circuit elements can be approximated in such a way that they can be represented by resistors, capacitors, and inductances. If this is the case, one can intuitively understand the circuit. The famous Butterworth-van Dyke (BvD) circuit [66] (Fig. 7) can be derived from the Mason circuit. While the general form of the BvD circuit can be guessed without going back to the Mason circuit, the values of its elements can only be determined by the full derivation (Appendix A). 

The MMW electrical properties of the cavity and the oscillator at resonance are effectively fixed in their manufacture. This treatment addresses the coupling between those two circuit elements to achieve optimal performance. It considers only the circuits at resonance that is, under the working condition of the spectrometer. Recall that the capacitive and inductive reactances in a tuned circuit at resonance cancel each other yielding a purely resistive circuit element. Nonetheless the reactances both still remain and are manifest in the property Q. The treatment will yield the reflection coefficient p of the coupling interface between the cavity and oscillator in terms of their gs and the mutual inductance coupling coefficient M of the impedance transformer that the interface represents. Optimum performance will be when the two circuit elements are critically coupled to each other and that will be shown to occur when p = 0. 

The equivalent electrical circuit, rearranged under the influence of an apphed physical field, is considered as a parallel resonant circuit coupled to another circuit such as an antenna output circuit Thus, in Figure 15.4c, Wj, Cd, La, and Ra correspond to the circuit elements each Wd represents active emitter-coupled oscillator and Cd, Ld, and Rd, represent passive capacitive, inductive, and resistive elements respectively. The subscript d is related to the particular droplet diameter, that is, the droplet under consideration. Now, again the initial electromagnetic oscillation is represented by... 

Inductance is, primarily, a geometrical property of a current-carrying element in an electrical circuit. A circuit element with this property may be termed an inductor. The magnitude and, for that matter, the frequency dependence of inductance, also depend on the material environment of that element. Similar... 

Mutual inductance The magnetic flux linkage common to two magnetic circuit elements per unit current flowing through the element in question. 

At the self-neutralizing frequency, the tetrode or pentode is inherently neutralized by the circuit elements within the device itself, and external screen inductance to ground. When a device is operated... 

Inductive A circuit element exhibiting inductive reactance. 

Both capacitive reactance and inductive reactance are frequency-dependent quantities. At low frequency when the rate of change in current is low, the effects of inductive reactance in most of the components of a circuit are sufficiently small to be neglected. With rapid changes, on the other hand, circuit elements such as switches, junctions, and resistors may exhibit inductive reactance. Capacitwe reactance, on the other hand, is largest at low frequencies and decreases with increasing frequency. Reactance effects may be undesirable and a result of capacitance and inductance inherent in components. Attempts arc made to minimize reactance in such circumstances. 

The irreversible conversion of electrical energy into heat in electrical circuit elements, such as resistors, capacitors and inductances also leads to entropy production. The thermodynamic formalism of circuit elements can be developed by considering the changes in the energies associated with them. Section 10.1 showed that in the presence of a field we have... 

Figure 17.3 Elementary circuit elements, such as a resistor R, a capacitor C and an inductance L, also dissipate energy and produce entropy. In the thermodynamic formalism there are no ideal circuit elements with no dissipation of energy. Linear phenomenological laws give expressions for the rate of entropy production and dissipation of energy...

Using equations (17.1.28) and (17.1.29) obtain the time variation of I(t) and Q(t) in a real capacitor and a real inductance. Using these expressions in (17.1.25) and (17.1.26) obtain the entropy production at any time t in these circuit elements with initial current Iq and initial charge Qo-... 

Choosing a thickness-polarized, thickness-vibrating piezoelectric element as an example, we can define the applied voltage V, current i, dimensions b, h, and /, and the output force and velocity F and the cross-sectional area bounded by b and / can be defined by A here it is assumed this area is electroded on the top and bottom faces of the element and that b and / are much greater than h. Treating it as a collection of discrete circuit elements as shown in Fig. lb, the Van Dyke circuit, allows the analysis of one resonance within the isolated element. Most piezoelectric materials are capacitive insulators, and the shunt capacitance Cs = bl/p h is the constant capacitance present across the element. The additional branch in the circuit represents the specific resonance being analyzed, the motional branch with inductance L, resistance R, and capacitance C. Many impedance analyzers provide this circuit as a means to model the electrical behavior of the piezoelectric element. The coupling coefficient for this... 

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. 

Resistance, R, capacitance, C, and inductance, L, are all observable phenomena used in circuit elements. They result from the motion of electrons in solids and their interaction with each other and with the atoms surrounding them. Each also depends upon the geometry of the circuit element producing the effect. The basic materials properties, however, are dependent only upon the electronic structure in that material and not on the geometry. These underlying properties are the resistivity, p, of a... 

This Chapter reviews some of the basic physics and operation of selected circuit elements used in microelectronic devices. For a complete review, see the suggested readings. Basic resistance, capacitance, and inductance were covered in Chapter 2. We focus here on diodes, including clas-sic homojunctions, heterojunctions, and Schottky barriers, because they illustrate most of the important issues in microelectronic materials and because both field-effect and bipolar junction transistors are constructed from them. Once we have discussed diodes, a brief review of these two major classes of transistors is provided. Finally, we finish the review with some of the issues unique to light emitting and laser diodes. 

Foxboro s Model 823 transmitter uses a taut wire stretched between a measuring diaphragm and a restraining element. The differential process pressure across the measuring diaphragm increases the tension on the wire, thus changing the wire s natural frequency when it is excited by an electromagnet. This vibration (1800—3000 H2) is picked up inductively in an oscillator circuit which feeds a frequency-to-current converter to get a 4—20 m A d-c output. 

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