Lumped Capacitance

On the supply side of the interrupter, an equivalent busbar, inductance and lumped capacitance with a provision to connect p.f. correction capacitors, if required, to represent a replica of the actual installation. 

Cs - Lumped capacitance of the lower voltage side C - Protective capacitance... 

Vk = voltage of surge transference Cp = lumped capacitance between the primary and the secondary windings... 

C = lumped capacitance of the lower voltage side = prospective voltage surge on the primary side /) = a factor to account for the power frequency voltage already existing w hen the surge occurs... 

I Shunt reactors These are provided as shown in Figure 24.23 to compensate for the distributed lumped capacitances, C , on EHV networks and also to limit temporary overvoltages caused during a load rejection, followed by a ground fault or a phase fault within the prescribed steady-state voltage limits, as noted in Table 24.3. They ab.sorb reactive power to offset the charging power demand of EHV lines (Table 24.2, column 9). The selection of a reactor can be made on the basis of the duty it has to perform and the compensation required. Some of the different types of reactors and their characteristics are described in Chapter 27. 

Figure 5. Simplified drawings of sample cells, (a) Open coaxial line cell (b) lumped capacitance cell (c) open-ended coaxial cell. (Reproduced with permission from Ref. 113. Copyright 2000, Marcel Dekker, Inc.)...

Lumped Capacitance of inter-chip contact (fF) Bus Wire Delay (ns) Critical Path Delay (ns) Clock Frequency (MHz) Improvement to 2D Solution... 

When the Biot number is sufficiently small (Bi < 0.2), the series solutions converge to the first term for all values of Fo > 0. The values of the Fourier coefficients A, and B, approach 1, and the dimensionless temperature and the heat loss fraction approach the general lumped capacitance solutions... 

The deforce model of Equation 3.29 can be extended approximately to include low frequency ac fields for an array of semi-insulating particles using lumped capacitance. Colver and Wang, 1994, show approximately that... 

Figure 5 Simplified drawings of sample cells (a) open coaxial line cell (b) lumped capacitance cell (c) end capacitance cell.

Figure 3. Simplified schematic drawings of dielectric sample cells for reflection measurements, (a) Lumped capacitance cell, (b) End capacitance cell, (c) Open coaxial line cell, (d) Coaxial line cell with 50 ohm termination. Bottom sections in all cases are 50 ohm 7 mm precision coaxial lines.

The mass and heat transfer of an evaporation process determine the drop size and drop temperature. Both of these quantities require a description that is numerically efficient but sufficiently accurate so that averages taken over the chosen sampling sizes reflect realistic values. In order to be able to compute drop sizes and temperatures for millions of droplets (or, after discretization of the PDF, for tens of thousands of parcels), various simplifying assumptions have to be made. One of the most common assumptions is the lumped capacitance assumption which states that the temperature within the droplet is spatially uniform and only depends on time. This assumption is satisfied if the Biot number, defined as the ratio of heat transferred to the droplet over heat conducted inside the droplet, is small. More formally, this is expressed as (cf. Incropera and DeWitt [14])... 

It is assumed that the IPMC is composed of an IP film sandwiched between two perfectly conductive metal electrodes. The linearized PNP model is used to describe the dynamics of the electric potential and the concentration of the mobile counterions within the polymer. In the case of the fiat electrodes, by solving the partial differential equation based on the PNP model, the equivalent circuit, which is composed of the following lumped capacitances - the double-layer capacitance, Cj, the bulk capacitance Q, and the bulk conductance, Si (see Fig. 6a) - can be obtained (Aureli and Porfiri 2012). 

Fig, 6 Equivalent circuits of the IPMC. (a) Lumped capacitance and resistance model, (b) Distributed circuit model that takes into account the roughness of the plated electrodes, (c) A possible distributed circuit model that takes into account the surface resistance of the plated electrodes, (d) A possible circuit model that takes into account the ion transport in the porous electrodes... 

CB, DS, transformer, and bushing ACB and a DS are represented by lumped capacitances between the poles and to the soil. A transformer is also represented by a capacitance to the soil unless a transferred surge to the secondary circuit must be calculated. Abashing is represented by a capacitance or, occasionally, a distributed line. 

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