DC and AC Currents

Direct current (DC) in an electric circuit describes a unidirectional flow of electrons traveling continuously from a low to high potential area. The relationship between the direct current I and the difference between high and low potentials V are described as follows. If there are two points designated 1 and 2 along a circuit wire loop, the potential of Point 1 is Vj and that of Point 2 is V2 (i.e., the potential difference or voltage difference between these two points is y = V2 11 )i when a current (I) flows from Point 1 to Point 2, the relationship between I and V can be expressed as 

This relationship is called Ohm s Law, where R is the electric resistance expressed in ohm (fl) units if the unit of current is the ampere (A) and the potential difference is voltage (V). According to Ohm s law, in practice, some specifically designed resistors using appropriate materials are fabricated and connected inside the electric loop to control current flow. 

Length of wire I with cross-sectional area S through which an established current travels. 

If a material has a pure electric resistance property, it is considered an ohmic material and has a constant resistance R largely independent of the potential applied or the current passed through. Other materials that do not comply with Ohm s law have non-linear resistances. Ideal resistors are considered to have no function in storing energy via an electric or magnetic field. However, in AC applications, this is hardly the case because an equivalent inductance or capacitance in series with the resistor element is often considered. The use of AC circuits requires the consideration of additional opposition to current flow due to electrical and magnetic fields treated as electrical reactance effects. An electrical circuit s impedance is defined by the sum effect of resistance and resistance [3]. 

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Nineteenth-century records report successful electrochemical healing of broken bones (Stevens, 1812). The beginnings of a modem phase in this work are attributed to Brighton at the University of Pennsylvania (1966). The technique has been developed so that it is an accepted method in orthopedics. The beginning of a noninvasive technique using a Helmholtz coil to induce currents is attributed to Pilla (1974). Both dc and ac currents have been used. Typically, the methods employ pulses lasting 5 x 1(T3 s with a repetition rate of 15 per second. 

Apart from galvanic separation and the possibility of measuring both dc and ac currents, the closed-loop method has several other advantages. The range of currents being measured is much larger than in open-loop devices and only limited by how much current the feedback circuit can deliver. Since the sensor always... 

The mechanism of electrode polarization varies slightly for dc and ac currents. (The development which follows makes reference to Figure 2.2.) For the dc case, ions are attracted to the electrodes. An ionic interface layer is established between each electrode and the electrolyte. This process results in an apparent impedance for the solution which is different from the true impedance. The apparent impedance is somewhat higher than the true impedance, and one may consider that the polarization effect at the electrode surfaces contributes a series polarization impedance to the true impedance of the electrolyte. Other effects are discussed in Chapter 3. Electrode boundary... 

The working principle of a third type of mass filter, the ion trap detector (ITD), is illustrated in Fig. 6. It operates like the quadrupole based on the concept that the trajectories of ions, traveling in an oscillating electric field, become influenced by the wave frequency. Dissimilar to the quadrupole filter, however, the ion separation of the ITD occurs in a closed cavity, where the dc and ac currents applied to a ring electrode and an end cap of the cell set up the electric field. The molecules enter the cell in which they are ionized by an electron beam, and under the control of the given electric field the ions are forced to move in an orbit within the space of the cell. When the ac or dc potential is changed, the motion of some ions becomes unstable. 

In contrast to a direct injection of dc or ac currents in the sample to be tested, the induction of eddy currents by an external excitation coil generates a locally limited current distribution. Since no electrical connection to the sample is required, eddy current NDE is easier to use from a practical point of view, however, the choice of the optimum measurement parameters, like e.g. the excitation frequency, is more critical. Furthermore, the calculation of the current flow in the sample from the measured field distribution tends to be more difficult than in case of a direct current injection. A homogenous field distribution produced by e.g. direct current injection or a sheet inducer [1] allows one to estimate more easily the defect geometry. However, for the detection of technically relevant cracks, these methods do not seem to be easily applicable and sensitive enough, especially in the case of deep lying and small cracks. 

Figure 5-5 How DC and AC Return Currents Flow in a Proper Ground Plane...

As a first example, let us consider a metallic thermistor inserted in fig. 3, whose resistance is, in a first approximation, expressed as R(T)=Ro(l+aT). R(T) is the resistance of a PTC thermistor at a given temperature T, Ro is the resistance at To, and I represents a suitable DC (or AC current), while A is the constant gain of a low noise amplifier, operating in a suitable bandwidth. Let us suppose that the injected current I does not induce, through the heating process, a detectable change of the resistance value. 

Lynntech, Inc. s (Lynntech s), electrokinetic remediation of contaminated soil technology is an in situ soil decontamination method that uses an electric current to transport soil contaminants. According to Lynntech, this technology uses both direct current (DC) and alternating current (AC) electrokinetic techniques (dielectrophoresis) to decontaminate soil containing heavy metals and organic contaminants. A non homogeneous electric field is applied between electrodes positioned in the soil. The field induces electrokinetic processes that cause the controlled, horizontal, and/or vertical removal of contaminants from soils of variable hydraulic permeabilities and moisture contents. 

In drawing an appropriate equivalent circuit, it is clear that the resistance of the solution should be placed first in the intended diagram, but how should the capacitative impedance be coupled with that of the interfacial resistance One simple test decides this issue. We know that electrochemical interfaces pass both dc and ac. It was seen in Eq. (7.103) that for a series arrangement of a capacitor and a resistor, the net resistance is infinite for = 0, i.e., for dc. Our circuit must therefore have its capacitance and resistance in parallel for under these circumstances, for = 0, a direct current can indeed pass the impedance has become entirely resistive.51... 

Fig. 5.14 The DC and AC polarographic circuits (a) and the current-potential curves for DC and AC polarographies (b).

In order to understand electrochemical impedance spectroscopy (EIS), we first need to learn and understand the principles of electronics. In this chapter, we will introduce the basic electric circuit theories, including the behaviours of circuit elements in direct current (DC) and alternating current (AC) circuits, complex algebra, electrical impedance, as well as network analysis. These electric circuit theories lay a solid foundation for understanding and practising EIS measurements and data analysis. 

The resistive shunt is a calibrated resistor placed in the current path (Fig. 7.19.2). According to Ohm s law the voltage drop across the resistor is directly proportional to the current. Highly linear and stable resistors are used as shunts to minimize deviations from Ohm law. A differential amplifier supplies the signal for further processing. This method can be used to measure both direct current (dc) and alternating current (ac). 

Finally, with the dc and ac components known, we can calculate the peak current using... 

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