Leakage Resistance

Equation (2.36) indicates that due to the leakage current and faradic leakage current, the current used to charge a supercapacitor is larger than expected and the current obtained from it is less than expected. Note that these two leakage current densities cause the self discharging of a supercapacitor, which is not desirable for practical applications. For a detailed discussion please see Reference 33. This faradic leakage current density is an 

Equivalent circuit of supercapacitor taking account of both ESR and leakage resistance. 

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As the tank fills the capacitance increases while the leakage resistance decreases in proportion to the wetted area. The conservative case is to consider only the floor area. Assume that the charging current Iq < 10 pA and that the gas involved is hydrogen, whose LMIE W = 0.016 mJ. Eor lining thickness d = 2 mm, dielectric constant = 4, and floor area A = 10 m, the... 

Equation (4) leads to a criterion for leakage resistance below which a specified energy W cannot be attained ... 

The electrical resistance of a coating on a pipeline will depend upon the effectiveness of its initial application to the metal and on its condition at the time of testing absorption of moisture may decrease the resistance by as little as 10% during a 2y-year period. The leakage resistance of a given section of pipeline can be determined by the following procedure ... 

Leakage resistance When dealing with low value currents, the leakage resistance of... 

An alternative design for cylindrical cells is the so-called inside-out configuration, in which the anode, in the form of zinc sheet vanes, is centrally placed and surrounded by the cathode mix. The principal advantage of this design is its high leakage resistance which results from the fact that the cell case is no longer fabricated from zinc. 

There are several things that need to be pointed out on this design. First, the upper electrode is porous, either because it is very thin (10-20 nm) or because it is deposited under such conditions that it cracks. In any case, the polymer beneath it comes into contact with the gas or vapor. Obviously, it is difficult to make robust electrical connections to the top electrode. Fortunately, it is not necessary because it forms an electrically floating plate, which is common to the two capacitors one between the Cr, Ni, Au plate (Ci) and the other between the top and the Ta plate (C2). The corresponding leakage resistances are R and R2. The response of this sensor to water vapor is shown in Fig. 8.14. 

Thurston G, Suri C, Smith K, et al, Leakage-resistant blood vessels in mice transgenically overexpressing angiopoietin-1. Science 1999 286 251 1-2514. 

When an a.c. voltage is applied to a perfect capacitor, no energy is dissipated. However, a real capacitor dissipates energy because of lead and electrode resistances, d.c. leakage resistance and, most importantly, dielectric losses. These account for the capacitor s dissipation factor or loss tangent tan 3. It is sometimes convenient to regard the lossy capacitor as an ideal capacitor shunted by a resistance Rp or in series with a resistance rs, as shown in Fig. 5.5. 

Usually the separation is effective in proportion to E because E represents either the amount of contaminant removed if the rejected solute is undesirable or the amount of product concentrated if the solute is desirable. However, the degree to which the concentration at the interface c0 can be increased to this end is limited because high values augment leakage, resistance to flow, and the risk of precipitation. Consequently, to increase E, efforts are generally made to increase effective diffusivity Dr, which is best done through stirring or convective processes. Thus these processes become important considerations to effective operation. 

T is estimated from the leakage resistance of the capacitor employed. 

Finally, it should be noted that in many cases where < 0, is determined by the capacity method uncertainty arises, which is related to the frequency dependence of Mott-Schottky plots. (In particular, the frequency of the measuring current is increased in order to reduce the contribution of surface states to the capacity measured.) As the frequency varies, these plots, as well as the plots of the squared leakage resistance R vs. the potential (in the electrode equivalent circuit, R and C are connected in parallel), are deformed in either of two ways (see Figs. 6a and 6b). In most of the cases, only the slopes of these plots change but their intercepts on the potential axis remain unchanged and are the same for capacity and resistance plots (Fig. 6b). Sometimes, however, not only does the slope vary but the straight line shifts, as a whole, with respect to the potential axis, so that the intercept on this axis depends upon the frequency (Fig. 6a). 

It is important to be able to calculate the system parameters from the model of the sensor. Let us determine the cut-off frequency for a piezoelectric sensor which has C = 400 pF and leakage resistance of 10 Gfi. The amplifier input impedance is 10 MS2. If we use the modified piezoelectric sensor equivalent circuit (figure 2.1(b)) for this calculation, we find that the cut-off frequency for this circuit is... 

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