Resistances in parallel

Conduction through Several Bodies in Parallel For n resistances in parallel, the rates of heat flow are additive ... 

Fig. 20.23 Analogy between a melal/solulion interface and a capacitance and resistance in parallel, (a) Non-polarisable electrode, e.g. Hg/KCI solution, (b) polarisable electrode, e.g.

Reynolds, O. Papers on Mechanical and Physical Subjects 2 (1881-1901) 51. An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and the law of resistance in parallel channels. 535. On the dynamical theory of incompressible viscous fluids and the determination of the criterion. 

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... 

A more complicated model situation is demanded if one thinks of the equivalent circuit for an electrode covered with an oxide film. One might think of A1 and the protective oxide film that grows upon it during anodic polarization. One has to allow for the resistance of the solution, as before. Then there is an equivalent circuit element to model the metal oxide/solution interface, a capacitance and interfacial resistance in parallel. The electrons that enter the oxide by passing across the interfacial region can be shown to go to certain surface states (Section 6.10.1.8) on the oxide surface, and they must be represented. Finally, on the way to the underlying metal, the electron... 

Resistances in parallel have overall an overall resistance whose reciprocal is the sum of the reciprocals of each resistance ... 

When the stomata are open, the cuticular resistance (r ) is usually much larger than the resistance in parallel with it, rj s 4- In that case, the leaf resistance as given by Equation 8.11 is approximately equal to 4- r, . 

O. Reynolds. On the Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and the Law of Resistance in Parallel Channels." Philosophical Transactions of the Royal Society of London 174 (1883), pp. 935-82. 

The resistance output of an instrument like the LKB conductolyser can be made more appropriate for conductivity measurements by connecting a resistance in parallel with the conductivity cell. This gives... 

Equation (2.10) shows that separate removal paths add together to give a total lifetime, like electrical resistances in parallel add to give a total resistance that is even smaller than the... 

A number of pathways are available from the quasi-laminar layer to the vegetation canopy or ground, including uptake by plant tissue inside leaf pores (stomata), the waxy skin of some leaves (cuticle), and mesophyll of leaves, deposition to the soil, and reactions with wetted surfaces. Each of these pathways can be represented by an appropriate resistance to transport the total canopy resistance rc is then determined by summing these resistances in parallel... 

The radioelectric properties of two composites based on polyaniline impregnated glass textiles with different conductivities have been characterised. Changes of (fi. e") with frequency are shown in Figure 8.41. A dependence quite different from those already presented is observed. Indeed, for both conductivities, log e" decreases linearly with log/ with a slope close to unity, e.g., 0.7 and 0.8. This behaviour, independent of conductivity, is representative of a purely resistive material. The electrical equivalent circuit was found to be a resistance in parallel with a capacitance [84,86]. 

Equation 2.8 can further be simplified to determine a characteristic K value. Recognizing resistances in parallel or conductance in series once again, the expression for is [4 = (Rbl(Rs + Rh)) i] can be simplified as i, = (Rb/Rs) i for concentrated bulk liquid systems where Rb Rs and that their ratio remain approximately constant. Alternatively, 4 = 0.5/ in dilute systems when Rb = Rs. Hence, based on the data reported by Shang, Lo, and Inculet (1995) and the treatise above, it can be said that 0.1/ < is < 0.5/ in most natural clay-electrolyte systems, with the assumption that surface conductivity can never be larger than the bulk conductivity. 

The total pressure drop in multicompartment baghouses operated in parallel, in terms of drag, is analogous to a set of electrical resistances in parallel [43] ... 

The hg involves convection and gas radiation to or from a surface, and it is like two resistances in parallel, thus hg = he + hr. Similar to Ohm s Law, (/ = E/Rt), heat flux, q = Q/A = ATfR, or g — UAAT, which is the basic equation of heat transfer. Example 5.1 illustrates the method for calculating U, the overall coefficient of heat transfer. 

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