Impedance resistor

Two difierent components contribute to impedance the resistive or real component due to resistors and the reactive or imaginary component from AC circuitry elements, such as capacitors, inductors, etc. Unlike the resistive component, the reactive impedance affects not only the magnitude of the AC wave but also its time-... 

In another type of measurement, the parallel between mechanical and electrical networks can be exploited by using variable capacitors and resistors to balance the impedance of the transducer circuit. These electrical measurements readily lend themselves to computer interfacing for data acquisition and analysis. 

Electrochemical Impedance Spectroscopy (EIS) and AC Impedance Many direct-current test techniques assess the overall corrosion process occurring at a metal surface, but treat the metal/ solution interface as if it were a pure resistor. Problems of accuracy and reproducibility frequently encountered in the application of direct-current methods have led to increasing use of electrochemical impedance spectroscopy (EIS). 

In maldug electrochemical impedance measurements, one vec tor is examined, using the others as the frame of reference. The voltage vector is divided by the current vec tor, as in Ohm s law. Electrochemical impedance measures the impedance of an electrochemical system and then mathematically models the response using simple circuit elements such as resistors, capacitors, and inductors. In some cases, the circuit elements are used to yield information about the kinetics of the corrosion process. 

To increase the impedance of the network, a series resistor or reactor is sometimes used to contain the fault level of a system within a desirable limit. This may be required to make the selection of the interrupting device easy, and from the available range, without an extra cost for a new design as well as an economical selection of the interconnecting conductors and cables. Such a situation may arise on HV >66 kV or EFIV > 132. kV transmission networks, when they are being fed by two or more power sources, which may raise the fault level of the system to an unacceptable level. The cost of the interrupting device for such a fault level may become disproportionately high, and sometimes even pose a problem in availability. 

These transformers are three-phase and may be connected for zig-zag or star/delta connections (Section 20.9.1). The delta may also be made open type by inserting a resistor across it to help adjust the zero-sequence impedance, if required. 

IZI=J(Z )2+(Z ), and phase angle shift,, vs. f). The electrochemical system is then simulated with an electrical circuit that gives the same impedance response. Ideally this electrical circuit is composed of linear passive elements, e.g. resistors and capacitors, each of which represents individual physicochemical steps in the electrochemical reaction. ... 

We found an equivalent electrical circuit that fits best the LixC6 electrode behavior at high frequency. The circuit consists of a resistor R in parallel with a constant phase element (CPE). The latter is defined with a pseudo-capacitance Q and a parameter a with 0< a <1 [6], The impedance of... 

To analyse the response of this circuit to an alternating voltage, it turns out to be rather easier to replace the simple sinusoidal form of the voltage used above by V = V e ", where the complex number e,w = cos wt + t sin wt and i = J — 1 Any component of a circuit such as that shown can be defined as having an impedance Z, which can also be thought of as a complex number, containing both phase and magnitude information. For a resistor, Z is entirely real and simply equal to the resistance R, but for a capacitor ... 

The general nexus between fluctuation and dissipation was examined by Callen and Welton [122] in terms of the fluctuations of appropriate generalized forces and the impedance in a linear dissipative system. A system is considered to be dissipative if capable of absorbing energy when subjected to a time-periodic perturbation, e.g. an electrical resistor that absorbs energy from an impressed periodic potential. 

In order to allow the resistance measurement, the current injection is obtained in the circuit represented in fig. 3, by applying a voltage Vo- This current, due to the virtual ground condition determined by the circuit configuration (very high input impedance), will cross the feedback resistor Rf and determine an output voltage. In this example M and Yj (j=l,2,3) are the quantities ... 

At the heart of impedance analysis is the concept of an equivalent circuit. We assume that any cell (and its constituent phases, planes and layers) can be approximated to an array of electrical components. This array is termed the equivalent circuit , with a knowledge of its make-up being an extremely powetfitl simulation technique. Basically, we mentally dissect the cell or sample into resistors and capacitors, and then arrange them in such a way that the impedance behaviour in the Nyquist plot is reproduced exactly (see Section 10.2 below on electrochemical simulation). 

The resistance R) may be defined as an impediment to the flow of electronic charge. Consider a pure resistor (that is, one having no capacitance whatsoever) its resistance when determined with a continuous current is R, and its impedance is frequency-independent. We can say that ... 

Worked Example 8.3. What is the impedance of a pure resistor having a resistance / of 1.2 X lO-" ... 

Platinum wire is used to make an electrode, with the metal behaving as a pure resistor. If the resistance of platinum is 1 2 per cm (in length) and the electrode is 7 mm long, what is (a) its resistance and (b) its impedance ... 

As a rule, when thinking in terms of genuine electrical components, rather than pure ones, we can still say that the real impedances Z behave largely like resistors while the imaginary impedances Z" behave largely like capacitors. 

The total resistance of several resistors placed in series (Figure 8.11(a)) is simply the sum of the individual resistances. Similarly, the total impedance of a... 

Worked Example 8.5. Three pure resistors are joined together in series. What is the total impedance if R = 10, R2 = 210 and / 3 = 3.1 fi ... 

We notice that impedances, when combined in series, generate a bigger impedance than any of the constituents. We should also note that these values of Z may be a function of frequency if Z represents components other than pure resistors. 

Each of these layers behaves just like an RC element (that is, a capacitor and resistor in parallel) within the equivalent circuit (see Figure 8.13). The respective values o/R, and C, will be unique to each RC element since each layer has a distinct value of [H ]. In order to simplify the equivalent circuit, this infinite sum ofRC elements is given the symbol Zw or -W and is termed a Warburg impedance, or just a Warburg . The Warburg in Figure 8.12 extends from about 50 down to 15 Hz. 

It should also be mentioned that capacitors were then added in parallel with the resistors in equivalent circuit elements because the frequency-dependent experimental electrical impedance data had a component that was 90° out of phase with the resistor. 

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