AC resistance

Since the Wenner rod is mechanically somewhat delicate, it is only used in loose soils or in bore holes. For all measuring rods, the specific soil resistivity is equal to the product of the measured ac resistance and the shape factor Fq, which is determined empirically. 

Nickel-cadmium cells have a very low ac resistance of 1 mil. The charge state of the cells is of secondary importance. Nickel-cadmium cells must have sufficient current capacity and have current stability. They can be used directly as a dc decoupling device (Fig. 14-6) [6]. 

As one can see, the larger-diameter wires suffer a much more rapid degradation in ac resistance with increasing frequency than do smaller-diameter wires. So it is advantageous to use multiple strands of smaller wires instead of one large diameter wire. The ac current density of the smaller wires (>30 AWG) can actually be pushed to two to three times the assumed current density used in the charts because their surface area to cross-sectional area ratio is much greater. 

The ac resistance increase due to skin effect given above should be considered as a minimum. When wires are placed next to one another and placed in layers within a transformer, the near field magnetic effects between wires further crowd the current density into even smaller areas within the wire s cross-section. For instance, when wires are wound next to one another, the current is pushed away from the points of contact along the surfaces of the wires to areas orthogonal to the winding plane. When layers are placed on top of one another the inner layers show much greater degradation in apparent resistance than do the outermost layers. 

Figure 13. Schematic diagram of the measurement of the ionic conductivity of a conducting polymer membrane as a function of oxidation state (potential), (a) Pt electrodes (b) potentiostat (c) gold minigrid (d) polymer film (e) electrolyte solution (0 dc or ac resistance measurement.133 (Reprinted with permission from J. Am Chem Soc. 104, 6139-6140, 1982. Copyright 1982, American Chemical Society.)...

The most important non-faradaic methods are conductometric analysis and (normal) potentiometric analysis in the former we have to deal essentially with the ionics and in the latter mainly with the electrodics. Strictly, one should assign a separate position to high-frequency analysis, where not so much the ionic conductance but rather the dielectric and/or diamagnetic properties of the solution are playing a role. Nevertheless, we shall still consider this techniques as a special form of conductometry, because the capacitive and inductive properties of the solution show up versus high-frequency as a kind of AC resistance (impedance) and, therefore, as far as its reciprocal is concerned, as a kind of AC conductance. 

AC resistance effects are a little more complicated than that, I would have thought. 

Figure 5-6, and tries to couple very closely with the forward trace. In doing so, it attempts to cancel the fields produced by the forward trace. It is nature s way of helping us, if we just let it. We should realize that inductance exists only because of the field it produces and vice versa. The field contains the associated stored energy of 1/2 x LI2. Then if the field is somehow canceled, so is the inductance. Proximity effects are also minimized by the paralleling of these opposite traces, and therefore AC resistance is also reduced. 

The so-called 1-oz board in the USA is actually equivalent to 1.4 mils (35 tm) copper thickness. Similarly the 2-oz board is twice that. For a moderate temperature rise (less than 30°C) and currents less than 5A, we can use a minimum llmils width of copper per amp for 1-oz board, and at least 7mils width of copper per amp for a 2-oz board. This rule of thumb is based on the DC resistance of the trace only. So to decrease its inductive impedance and AC resistance, higher trace widths may be required. 

Therefore, the strip was sticking out from the Cu top to avoid oscillations of the sample, the second copper block (D) was tied to a fibreglass stick (E) attached to the copper top by means of a thin PTFE wire (F) of negligible thermal conductance. The electrical connections of the thermometer (TH) and the heater (FI) was made by eight manganin wires (G), 100 xm in diameter. Another thermometer (Tc) was used to monitor the temperature of the cold end of the sample. An LR700 AC resistance bridge was used to read the resistance of the thermometers. 

An AVS 47 AC resistance bridge for the thermometer and a four-wire I-V source (Keitley 236) for the heater were used. The contributions to the addendum are reported in Table 12.2. 

For all the runs, a calibrated NTD Ge 34B thermistor (3x3x1 mm3) and a Si heater have been used. Electrical connections were made by means of superconducting NbTi wires 25 xm in diameter. The connection between the gold wires of both thermistor and heater and the NbTi leads was done by crimping the wires in a tiny A1 tube (0.1 mg). At the ends of the NbTi wires, a four lead connection was adopted. An AVS47 AC resistance bridge has been used for the thermometry and a four-wire I-V source meter (Keithley 236) for the Si heater was used. 

This equation indicates that the coil sensitivity varies inversely with the diameter of the coil (for a fixed length-to-diameter ratio). For diameters below 3mm, the AC resistance of the coil itself acts as the major noise source, even for lossy biological samples. The resistance depends on both the winding geometry (including wire diameter, number of turns, and turn spacing) and the resistivity of the conductor. 

Conventional two-electrode dc measurements on ceramics only yield conductivities that are averaged over contributions of bulk, grain boundaries and electrodes. Experimental techniques are therefore required to split the total sample resistance Rtot into its individual contributions. Four-point dc measurements using different electrodes for current supply and voltage measurement can, for example, be applied to avoid the influence of electrode resistances. In 1969 Bauerle [197] showed that impedance spectroscopy (i.e. frequency-dependent ac resistance measurements) facilitates a differentiation between bulk, grain boundary and electrode resistances in doped ZrC>2 samples. Since that time, this technique has become common in the field of solid state ionics and today it is probably the most important tool for investigating electrical transport in and electrochemical properties of ionic solids. Impedance spectroscopy is also widely used in liquid electrochemistry and reviews on this technique be found in Refs. [198 201], In this section, just some basic aspects of impedance spectroscopic studies in solid state ionics are discussed. 

The alternating current (AC) resistivity of LDPE film does not change with water immersion even under electrical stress of lOkV/mm as shown in Figure 24.10, where the relative resistivity is plotted as a function of immersion time. The figures indicate that liquid water does not cause the breakdown of the surface state consisting of the three phases. 

When an LDPE film is immersed in a salt solution (0.9% NaCl), the AC resistivity decreases as a function of the immersion time, as shown in Figure 24.11. These figures include the effect of a nanofilm of plasma polymer deposited on the surface of LDPE. With hydrophobic plasma polymer (HFE + H2), the decrease of AC resistivity was not observed. These figures indicate that the surface state breakdown occurs when the salt intrusion takes place. The salt intrusion can be prevented by the application of a plasma polymer, which is an amorphous network (one phase and no weak boundary). The extent of protection seems to be dependent on the hydrophobicity of the network. 

Figure 24.10 AC resistivity ratio versus aging time for untreated LDPE films in a deionized water environment (a) unstressed, and (b) lOkV/mm stressed.

Figure 24.12 AC resistivity ratio vs. aging time for 5kV/mm stressed samples in a 0.9% saline solution (a) untreated, (b) CH4 treated, (c) C2F6 + H2 (1 1 ) treated.

S. Ottow, G. S. Popkirov, and H. Foil, Determination of flat-hand potentials of silicon electrodes in HF by means of AC resistance measurements, J. Electroanal. Chem. 455, 29, 1998. 

As frequency increases, d decreases, causing the wire to present a smaller cross-sectional area. This increases the ac resistance and consequently lowers the circuit Q. NMR coils are often made of flat wire rather than normal round wire, the former also having the advantage of better rf homogeneity. The magnitude of the induced B i field is related to the power applied, Q, and the coil volume, V, by... 

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