The basic principles of Electrochemical Impedance Spectroscopy (EIS).
For any electric circuit, which consists of various passive elements (i.e. resistors, capacitors and inductors) the behaviour of the whole circuit to an applied ac voltage, is dependent upon both the behaviour of individual elements, and also on their arrangement in the circuit with respect to each other. If a dc direct voltage is applied to the elements that comprise the equivalent circuit, the resulting current can be measured using Ohms law.
For the case where a low amplitude sine wave Eac, of a particular frequency, is applied across a passive element, then:
E ac = E0 sin(ω t) (1)
Where:
Eac = potential at time t;
E0 = maximum voltage amplitude; ω = is the angular frequency, ω = 2πf; t = is the time.
Under these conditions, the resulting current response of a sine wave Iac will be given by:
I ac = Eac /X …. (2)
Where:
Iac = current at time t;
X = the reactance of the particular passive element in the electrical circuit.
When the applied signal is a sinusoidal voltage wave and the resulting signal is a sinusoidal current wave, then X is called the impedance Z; conversely, when the applied signal is a sinusoidal current wave, the resulting signal is a sinusoidal voltage wave, X which is called the admittance Y.
The value of the reactance of a capacitor or an inductor can be expressed as a complex quantity by the complex operator j, j = −1 [11], and using this notation the reactance of the elements are given by [12]:
For a resistor: XR = R
For a capacitor: XC = 1/-jωC
For an inductor: XL = jωL ………… (3-4)
For the impedance, Z(ω), as mentioned above...
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...ooking at the response of actual real-world systems. In some systems, the Nyquist plot was expected to be a semicircle with the center on the X -axis. However, the observed plot was indeed the arc of a circle, but with the center some distance below the x-axis.” “These depressed semicircles have been explained variously by a number of phenomena depending on the nature of the system being investigated. However the common thread among these explanations is that some property of the system is not homogeneous or that there is some distribution (dispersion) of the value of some physical property of the system. The CPE is usually represented by two parameters, Q° and n”. “It is tempting to simply associate the value of Q° for a CPE with the capacitance value, C, for an equivalent capacitor. The value range of n is between 0 and 1. When n = 0, Q° = R. When n = 1, Q = C.”
Oscilloscope is acquainted as one of the most helpful instrument for testing circuits. It is able to show the signals at different points in the circuit. One way to inves...
2-frequency:- as the frequwncy of the applied voltage increase, the dielectric strength will reduce. 3-the exisistence of humidity lead to decrese dielectric strength. 4-also the presence of surface defect like crack ,pore, decresing the dielectric strength.[53]
Dielectric materials are insulators that make it harder for the electric field to penetrate the space within a capacitor; this is due to the theory of polarization. In Lab 4 (Parallel Plate Capacitor), the objective was to measure the dielectric constant (κ) of a textbook (paper) using a makeshift capacitor of aluminum foil. This was done through graphical analysis by the linearization of equation (1). The goal was to construct a linear graph in which the slope and slope error was calculated using the Linest function, the slope than allows for the derivation of the dielectric constant of the paper in a textbook. Error propagation (error formulas) was also used in this lab to account for sources of errors that could have occurred.
In this case, the circuit will be analysed using a standardized Mesh Analysis using Kirchhoff’s Voltage Law. Indicated in the Figure 1 below are the loop directions (estimated) and the points for analysis of current and voltage have a sun shape about them.
By using the equation, 'Cu² - 2e’ Cu (s)' and the formula Q = I x T
The only problem with this experiment is that when the current passing through the battery circuit was at a continual rate there was...
Resonance means the certain way which a system moves at larger amplitudes at some frequencies than others. Resonance was originally discovered by Galileo Galilei. The response of resonance, especially for frequencies far from the resonant frequency depends on the detail of physical system and usually not identical to the resonant frequency. Television is an example of resonance which happens when the incomi...
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The concept of a low-pass filter exists in many different forms, including electronic circuits, digital algorithms for smoothing sets of data, blurring of images, acoustic barriers, and so on. Low-pass filters play the same role in signal processing that moving averages do in some other fields, such as finance; both tools provide a smoother form of a signal which removes the short-term oscillations, leaving only the long-term trend. The inductors and capacitors are the reactive elements of the filter. The number of elements determines the order of the filter.
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