AC circuits

Golde, R.H., Lightning surges on overhead disiribuii(m lines caused by direct and indirect lightning strikes. AIEE Transactions (Power Apparatus and Systemi. 437-447. June (1959) IRC. 56-HV AC Circuit Breakers. 

ANSI STANDARD DEVICE FUNTION NUMBER 52 AC CIRCUIT BREAKER... 

Peach, N., Electricity 12 What Phase Means in AC Circuits, Power, p. 138, July (1957). 

Electrical Units 278. Electrical Circuit Elements 281. Transient and AC Circuits 284. AC Power 285. Magnetism 286. Transformers 288. Rotating Machines 289. Polyphase Circuits 293. Power Transmission and Distribution Systems 294. 

In a transient or an AC circuit we term the sum of resistance, inductance, and capacitance as impedance. Using complex notation, the energy storage properties of inductance and capacitance are represented as purely imaginary quantities, while the resistance is represented as a (+) real quantity. Capacitance is represented as the negative imaginary axis, and current through a pure capacitance is said to lead... 

The power dissipated in an AC circuit with current of maximum amplitude flowing through a resistance is less than the power produced by a constant DC current of magnitude flow ing through the same resistance. For a sinusoidal AC current, the root mean square (rms) value of current I is the magnitude of the DC current producing the same power as the AC current with maximum amplitude I. The rms value I is given by... 

The power dissipated in an AC circuit with only resistive elements is... 

A model for the ac response of real electrodes is the simple electric equivalent circuit consisting of a resistance R and capacitance Q conneeted in series (Fig. 12.12a). It follows from the rules for ac circuits that for this combination... 

For the calculations, the capacitive (reactive) impedances = l/coC and Xp = 1/coCp are often used instead of capacitances and C. The impedance (admittance) of an ac circuit can be stated in terms of a complex number where the... 

For both H.F. modes a choice can be made from a few possibilities of measurement, viz., the observance of voltage and current in the ac circuit at a frequency imposed externally, or the establishment of internal resonance conditions where... 

In the ac circuit of the polarographic cell there is such an external ohmic resistance that via the alternating voltage (300 V) together with a superimposed dc the voltage over the cell alternates from 0 to -2V vs. an SCE within these limits oxidation of Hg and reduction of Na+ (electrolyte) to Na(Hg) remains sufficiently restricted. 

A recorder with inadequate shielding from AC circuits would display shifting of its zero point, and... 

Besides, it is also equally important to adjust properly the amplifier gain so as to eliminate completely the dead-band and the oscillations. A recorder having inadequate shielding from the AC circuits may display... 

The important point is that capacitors will, therefore, allow the flow of AC in preference to DC. Because there is less time for current to decay in a high-frequency AC circuit before the polarity reverses, the mean current flow is greater. The acronym CLiFF may help to remind you that capacitors act as low-frequency filters in that they tend to oppose the flow of low frequency or DC. 

Graphs show how capacitors alter current flow within a circuit. The points to demonstrate are that DC decays rapidly to zero and that the mean current flow is less in a low-frequency AC circuit than in a high-frequency one. 

When the current in a circuit is alternating rapidly, there is less time for exponential decay to occur before the polarity changes. This diagram should demonstrate that the mean positive and negative current flows are greater in a high-frequency AC circuit. 

A graph of current flow versus time aims to show how an inductor affects current flow in a circuit. It is difficult to draw a graph for an AC circuit, so a DC example is often used. The key point is to demonstrate that the back EMF is always greatest when there is greatest change in current flow and so the amount of current successfully passing through the inductor at these points in time is minimal. 

Capture and PSpice can be used to easily calculate the Norton and Thevenin equivalents of a circuit. The method we will use is the same as if we were going to find the equivalent circuits in the lab. We will make two measurements, the open circuit voltage and the short circuit current. The Thevenin resistance is then the open circuit voltage divided by the short circuit current. This will require us to create two circuits, one to find the open circuit voltage, and the second to find the short circuit current. In this example, we will find the Norton and Thevenin equivalent circuits for a DC circuit. This same procedure can be used to find the equivalent circuits of an AC circuit (a circuit with capacitors or inductors). However, instead of finding the open circuit voltage and short circuit current using the DC Nodal Analysis, we would need to use the AC analysis. 

In order to assimilate the following mateial, the reader should be familiar with a few simple concepts in instrumentation elecronics. These topics are more than adequately discussed in numerous texts and so we do not belabor them here. For the convenience of those who need to review, we have prepared a list of subjects essential to understanding these introductory sections. This list is all-inclusive, so study of topics not on the list (e.g., ac circuit theory, inductance, transformers, power supplies, digital electronics, transducers, transistors, etc.) will be of no immediate value. 

A method of avoiding the effect of potential differences arising at the electrodesolution interface is to take advantage of the capacitive behavior of the double layer at the electrode surface to make ac (alternating current) contact with the solution. To understand how this may be accomplished, it is necessary to consider a basic model of a conductance cell and examine its behavior under the influence of ac excitation. A review of ac circuit principles at a level sufficient for understanding the behavior of conductance cells and the instrumentation for conductance measurement is presented. The reader who desires a more thorough study of this topic is directed to material contained in the references [4-7]. 

All reactive power requirements are not necessary in every situation. Any electrical circuit or device when subjected to an electrical potential develops a magnetic field that represents the inductance of the circuit or the device. As current flows in the circuit, the inductance produces a voltage that tends to oppose the current. This effect, known as Lenz s law, produces a voltage drop in the circuit that represents a loss in the circuit. At any rate, inductance in AC circuits is present whether it is needed or not. In an electrical circuit, the apparent and reactive powers are represented by the power triangle shown in Figure 6.1. The following relationships apply ... 

Scientists and engineers frequently use diagrams to schematically represent electric circuits. A circuit exists when charge is able to flow around a closed path. There are two types of circuits direct current (DC) circuits and alternating current (AC) circuits. In DC circuits the current flows in one direction only, while in AC circuits the current periodically changes direction. DC circuits commonly use batteries, whereas most AC circuits get their energy from wall outlets or AC generators. We will discuss only DC circuits in detail in this textbook. 

In order to generalize the concept of resistance in alternate current (AC) circuits, the impedance is defined as follows [9]... 

G. Lancaster, Dc and ac circuits, Oxford Physics Series, Oxford University Press, 1973. 

Potential or current step transients seem to be more appropriate for kinetic studies since the initial and boundary conditions of the experiment are better defined unlike linear scan or cyclic voltammetry where time and potential are convoluted. The time resolution of the EQCM is limited in this case by the measurement of the resonant frequency. There are different methods to measure the crystal resonance frequency. In the simplest approach, the Miller oscillator or similar circuit tuned to one of the crystal resonance frequencies may be used and the frequency can be measured directly with a frequency meter [18]. This simple experimental device can be easily built, but has a poor resolution which is inversely proportional to the measurement time for instance for an accuracy of 1 Hz, a gate time of 1 second is needed, and for 0.1 Hz the measurement lasts as long as 10 seconds minimum to achieve the same accuracy. An advantage of the Miller oscillator is that the crystal electrode is grounded and can be used as the working electrode with a hard ground potentiostat with no conflict between the high ac circuit and the dc electrochemical circuit. 

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. 

In an AC circuit, assuming the voltage across the resistor is described by a sinusoidal wave (as shown in Equation 2.37), the current through the resistor, based on Ohm s law, is... 

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