Series and Parallel Circuits

From these simple expressions of ideal resistance and capacitance, intricate electrical networks can be assembled by applying the rules of series and parallel circuits ... 

Admittance-plane plots are presented in Figure 16.6 for the series and parallel circuit arrangements shown in Figure 4.3(a). The data are presented as a locus of points, where each data point corresponds to a different measurement frequency. As discussed for the impedance-plane representation (Figure 16.1), the admittance-plane format obscures the frequency dependence. This disadvantage can be mitigated somewhat by labeling some characteristic frequencies. 

FIGURE 16.19 Thermocouples in series and parallel circuits (a) thermopile for magnifying EMF when measuring small temperature differences, and ( >) parallel arrangement for sensing average temperature level. 

A combination drcuit is an electrical drcuit that contains both series and parallel circuits. 

A combination circuit takes the characteristics of both the series and parallel circuits and combines them to accomplish the desired result. Most circuits constructed in todays electrons use the combination circuit. 

The only two basically different versions are illustrated in Figure 9.6. Both allow DC, and both guarantee current limitation at high frequencies. The detailed equations are found in the appendix (Section 12.2). The two circuits are very similar because it is possible to obtain the same immittance values for all frequencies with only two sets of component values. As we have seen, this was not possible with the two-component series and parallel circuits. Their descriptive powers are therefore identical, and a choice must be... 

An illustration of the calculations in series and parallel circuits is given in Example 2-1. 

Ohm s law and resistance in series and parallel circuits (V-I graphs for ohmic conductors Rj-=RNR2 stc. 

Fig. 10 Simple circuit diagrams of the different series and parallel association of molecular wires Mi and M2 discussed in the text. The two molecular wires are (a) bonded in series, (b) connected in parallel on the metallic pads, (c) forming a single molecule with one intramolecular node, and (d) forming a single molecule with two intramolecular nodes...

If a film is heterogeneous, there may be parallel paths of sohd transformations (Figure 9-15). A transformation process can be short circuited by the presence of a parallel process, and this can greatly accelerate solid-state transformations. These can also be simplified by considering them as series and parallel processes, and, as long as they are linear (first order in concentrations), the electrical analogs can be used (Figure 9-15). 

Figure 8.10 Resistance with series and parallel capacitors (a) circuit (b) frequency dependence of impedance.

Real circuits can have a combination of both series and parallel arrangements, which may or may not be readily reduced to simpler circuits. Let s try one of these more complicated situations. Imagine the circuit shown in Figure 10.10 in which Rt = R2 = R3 = R = 10 Q and V = 10 V. Let s find the total current that flows through this circuit. 

The reciprocal derivatives of the j/V curve under illumination at open circuit and short circuit represent the series and parallel resistances Rs and Rp, respectively, of the diode device. Of course, for non-linear effects in the diode, these quantities are not constant but depend on voltage V, current density j (illumination level), reverse saturation current density jtev, and temperature T. 

The electrical analogy may be used to solve more complex problems involving both series and parallel thermal resistances. A typical problem and its analogous electric circuit are shown in Fig. 2-2. The one-dimensional heat-flow equation for this type of problem may be written... 

There are two basic circuit connections series circuit and parallel circuit. If two or more circuit components are connected end to end, as shown in Figure 23a, they are connected in series. A series circuit has only one path for the electric current to ran through all of its components. If two or more circuit components are connected like the mngs of a ladder, as shown in Figure 23b, they are connected in parallel. A parallel circuit has different paths for the electric current through each of its components, with the same voltage across. 

We have discussed in the above sections Faradaic impedance and the correlation between Faradaic impedance and kinetic parameters. In general, one desires to separate the Faradaic impedance from Rel and Cd. Now we will focus on the extraction of Zf and the kinetic parameters from direct impedance measurements. This is based on the transformation between equivalent circuits in series and equivalent circuits in parallel. 

The a.c. impedance technique [33,34] is used to study the response of the specimen electrode to perturbations in potential. Electrochemical processes occur at finite rates and may thus be out of phase with the oscillating voltage. The frequency response of the electrode may then be represented by an equivalent electrical circuit consisting of capacitances, resistances, and inductors arranged in series and parallel. A simplified circuit is shown in Fig. 16 together with a Nyquist plot which expresses the impedance of the system as a vector quantity. The pattern of such plots indicates the type and magnitude of the components in the equivalent electrical network [35]. 

Example 1 Conduction with Resistances in Series and Parallel Figure 5-4 shows the thermal circuit for a furnace wall. The outside surface has a known temperature T2 = 625 K. The temperature of the surroundings... 

We can therefore calculate the relative permittivity and dielectric loss of a material from measured values of either equivalent series or parallel circuit components of a specimen. 

For any pair of non-adjacent vertices, the resistance distance is the effective resistance calculated according to the two classical Kirchhoff laws for series and parallel electrical circuits some examples of calculations are given in Box R-1 for ethylbenzene. 

Fig. 9. Simple electrical circuits illustrating the relationship between driving force, V, current flow, /, and resistance, R. (a) Simple series circuit, (b) More complex circuit with multiple resistances Ri connected in series and parallel fashion.

Many of the electrical engineering textbooks that include the subject of motors in their contents describe the eqnivalent circnit of an indnction motor as a series and parallel combination of resistances and reactances, see References 1 to 8. The eqnivalent circnit nsnaUy defines the situation for one of the three phases and so care needs to be taken to ensure that the final resnlts obtained apply to the complete motor. Care is also necessary in nsing the ohmic data from mannfacturers, they may have either star winding valnes or delta winding valnes and the choice may not be obvious. The equivalent circuit of most practical use is shown in Figure 5.1 for one star connected winding, where -... 

In multiple-cavity molds, series and parallel cooling circuits are used. Series cooling enters and cools one cavity, then moves to the next until all the cavities are cooled. The temperature of the water increases as it moves through the mold, and this results in non-uniform cooling. Parallel cooling, on the other hand, enters and exists all cavities simultaneously, thereby cooling all cavities at a uniform rate. Parallel cooling is thus the preferred method but it is not always possible due to limitations. 

The third factor that influences the performance of solar cell is the fill factor that relates to the microscale morphology of active layer, charge extraction layer, and posttreatment of deposition process (Guo et al., 2013). The fill factor will also influence the short-circuit current density and open-circuit voltage that are relative to internal series and parallel... 

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