Resistance, capacitance, and inductance

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 

Here A is the area of the capacitor plates and d is their separation or the thickness of the insulating (dielectric) material between them. 

As we will see below, resistivity is directly related to the mobility of charges in the material, the dielectric response to its polarizability, and the permeability to the magnetic moment of the constituent atoms. 

Conduction in solids can occur by motion of electrons or charged atoms (ions). Most of this section is devoted to electronic conduction but a brief mention of ionic conduction is in order. 

Fast ionic conductors are used as solid electrolytes in fuel cells and sensors. The search for fast ion conductors operating near room temperature is a matter of current electronic materials research. The practical small-scale application of some types of fuel cells as replacements for batteries may hinge on success in this search. 

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Frequency dependence of the three components of impedance (resistive, capacitative, and inductive), showing the resonance frequency co0 = (LQ y2. 

The second meaning of the word circuit is related to electrochemical impedance spectroscopy. A key point in this spectroscopy is the fact that any -> electrochemical cell can be represented by an equivalent electrical circuit that consists of electronic (resistances, capacitances, and inductances) and mathematical components. The equivalent circuit is a model that more or less correctly reflects the reality of the cell examined. At minimum, the equivalent circuit should contain a capacitor of - capacity Ca representing the -> double layer, the - impedance of the faradaic process Zf, and the uncompensated - resistance Ru (see -> IRU potential drop). The electronic components in the equivalent circuit can be arranged in series (series circuit) and parallel (parallel circuit). An equivalent circuit representing an electrochemical - half-cell or an -> electrode and an uncomplicated electrode process (-> Randles circuit) is shown below. Ic and If in the figure are the -> capacitive current and the -+ faradaic current, respectively. 

Table 39.2 lists the pressure-volume relationships for various geometries the fluidic capacitance is found simply by differentiating with respect to pressure. For small deformations, volume varies linearly with applied pressure, such that the capacitance is not a function of the pressure it merely defines the proportionality between increases in pressure and increases in stored mass. For such cases, the fluid circuit analysis is linear, because flow rate and pressure drops are related via linear expressions. For large deformations (i.e., the membrane limit), the fluidic capacitance is a function of the pressure this implies that the fluidic circuit behavior will be nonlinear. Obviously, once the fluidic resistance, capacitance and inductance have been identified via geometry (and material properties), complicated networks can be analyzed using commercially available circuit analysis software such as SPICE [42]. 

The respiratory system exhibits properties of resistance, compUance, and inertance analogous to the electrical properties of resistance, capacitance, and inductance. Of these, inertance is generally considered to be of less importance than the other two properties. 

Cooling effects Resistive, capacitive, and inductive effects effects Interferometers Sagnac effect Doppler effect... 

Figure 2.34 Voltage and current relationships in resistive, capacitive and inductive circuits...

The phenomenological equations for resistance, capacitance, and inductance are as follows. 

To understand the impedance of electrochemical objects, it is necessary to understand the behavior of simple electrical circuits, first in steady state, then in transient conditions. Such circuits contain simple linear electrical elements resistance, capacitance, and inductance. Then the cmicept of electrical impedance will be introduced. It demands an understanding of the Laplace and Fourier transforms, which will also be presented. To understand impedance, it is necessary to thoroughly understand the complex plane and Bode plots, which will be presented for a few typical connections of the electrical elements. They can be computed using Excel, Maple, Mathematica, and specialized programs such as ZView. Several examples and exercises will be included. 

Analysis of Eqs. (2.84), (2.86), and (2.87) reveals that the relation between current and potential in the presence of resistance, capacitance, and inductance may be represented in a general form ... 

Cable loss Signal loss caused by passing a signal through a coaxial cable. Losses are the result of resistance, capacitance, and inductance in the cable. 

When putting together a spectroscopy system, the term impedance will be encountered from time to time. For example, an amplifier output may be specified as 93 H impedance and it is important to have some appreciation of the significance of such statements. The impedance of a circuit or component, usually given the symbol Z, is a combination of resistance, capacitance and inductance. The units of impedance are ohms (H) and, for most practical gamma spectrometry purposes, impedance can be thought of as a resistance. 

IMPEDANCE A measure of opposition to time-varying electric current in an electric circuit depends on the resistance, capacitance and inductance of the circuit. 

For data interpretation an equivalent circuit model (see Figure 6.20) can be used consisting of resistive, capacitive, and inductive elements associated with several sources of polarization. In order to simplify the model, often elements associated with the anode are omitted as polarization resistance of the anode is much smaller compared to the cathode (Yan, 2007 Rubio, 2008 Asghari, 2010). 

Wireless biosensors for implantable or wearable sensors will be discussed in this chapter. The biosensors incorporating electrical measurements such as electrochemical transduction mechanism [potentiometric, amperometric, and field-effect transistor (FET)] and electrical transduction mechanism (resistance, capacitance, and inductance)... 

As a result of cavitation problems encountered in flow and pressure control valves used with liquid oxygen, it became necessary to develop some type of instrumentation which would accurately indicate the presence or absence of cavitation in the liquid oxygen flow through these valves. Various resistive, capacitive, and inductive principles were investigated in the development of this electronic cavitation detecting instrumentation, In addition to the normally low response of such instrumentation to the detection of density gradients in a liquid flow, the solution of this problem was further complicated by the difficulties encountered at the extreme low temperatures. 

An ideal electrode-electrolyte interface with an electron-transfer process can be described using Randle equivalent circuit shown in Fig. 2.7. The Faradaic electron-transfer reaction is represented by a charge transfer resistance and the mass transfer of the electroactive species is described by Warburg element (W). The electrolyte resistance R is in series with the parallel combination of the double-layer capacitance Cdi and an impedance of a Faradaic reaction. However, in practical application, the impedance results for a solid electrode/electrolyte interface often reveal a frequency dispersion that cannot be described by simple Randle circuit and simple electronic components. The interaction of each component in an electrochemical system contributes to the complexity of final impedance spectroscopy results. The FIS results often consist of resistive, capacitive, and inductive components, and all of them can be influenced by analytes and their local environment, corresponding to solvent, electrolyte, electrode condition, and other possible electrochemically active species. It is important to characterize the electrode/electrolyte interface properties by FIS for their real-world applications in sensors and energy storage applications. 

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. 

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