Capacitance, definition

Canine left ventricle model, 8 II Canlon.B., 63-11 Cannon, W.B., 6-7 Capacitance definition, 58-2 of venous system... 

Using the definition of differential capacitance (per unit area),... 

With the proper definitions of ex and k0, this equation is applicable to the metal as well as to the electrolyte in the electrochemical interface.24 Kornyshev et al109 used this approach to calculate the capacitance of the metal-electrolyte interface. In applying Eq. (45) to the electrolyte phase, ex is the dielectric function of the solvent, x extends from 0 to oo, and x extends from L, the distance of closest approach of an ion to the metal (whose surface is at x = 0), to oo, so that kq is replaced by kIo(x — L). Here k0 is the inverse Debye length for an electrolyte with dielectric constant of unity, since the dielectric constant is being taken into account on the left side of Eq. (45). For the metal phase (x < 0) one takes ex as the dielectric function of the metal and limits the integration over x ... 

The N-doped carbons with a nanotube backbone combine a moderate presence of micropores with the extraordinary effect of nitrogen that gives pseudocapacitance phenomena. The capacitance of the PAN/CNts composite (ca. 100 F/g) definitively exceeds the capacitance of the single components (5-20 F/g). The nitrogen functionalities, with electron donor properties, incorporated into the graphene rings have a great importance in the exceptional capacitance behavior. 

The double-layer charging current i may be calculated from the definitions of capacitance. 

This expression has a form exactly analogous to Ohm s law in dc circuits. The quantity l/toCs is called the capacitive reactance Xc. It is a measure of the opposition to the flow of charge in a capacitor, and it is therefore measured in ohms. If we now substitute the definition of Xc into the expression for ec, it follows that... 

Yet, apart from the purely quantitative criterion, one should also take into consideration general reasoning. When comparing the discussed methods, we note that the er 2 vs. E plot is frequency-independent indeed, this is because a is frequency-independent by definition [see Eq. (2)]. This plot is believed to be the most universal for comparing results of different experiments because the contribution, coming from the frequency-dependent factor proper, is separated in this case. Unfortunately, the dimensionality of a precludes a correct comparison of the results thus computed with the directly measured capacitance values published in the literature. 

Definition A condenser has the capacitance of 1 farad, when a charge of 1 - coulomb generates a voltage of 1 volt. 

When the impedance versus the reciprocal of the square root of the frequency is plotted, the slope gives (Rf/Cdi)U2, where Rp is the ionic resistance of the anode catalyst layer. The double-layer capacitance can be obtained from the cyclic voltammogram. According to the definition of capacitance, the capacitance of the double layer equals the current divided by the scan rate (Cdt = TV-1). The ionic resistance can be obtained from the capacitance of the double layer. 

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