Parallel combination

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

These are unidirectional and uncontrollablet static electronic devices and used as static switches and shown in Figure 6.14. A diode turns ON at the instant it becomes forward biased and OFF when it becomes reverse biased. By connecting them in series parallel combinations, they can be made suitable for any desired voltage and current ratings. Whether it is a transistor scheme or a thyristor scheme, they are used extensively where a forward conduction alone is necessary and the scheme calls for only a simple switching, without any control over the switching operation. They are used extensively in a rectifier circuit to convert a fixed a.c. supply to a fixed d.c. supply. 

The triac may, however, have some limitations in handling frequencies higher than normal. In such cases, they can be simulated by using two SCRs in inverse parallel combinations as illustrated in Figure 6.22(b). Now it is known as a reverse conducting thyristor. An SCR has no frequency limitations at least up to ten times the normal. The required voltage and current ratings are obtained by series-parallel connections of more than one thyristor unit. 

Figure 6.22(b) Use of two SCRs in inverse parallel combination to simulate a triac (reverse-conducting thyristors)... 

These ratings can be enhanced by connecting them in series-parallel combinations. In scries to enhance the voltage rating and in parallel to enhance the cuiTcnl rating. Bui the controls may not be so accurate as with a single device. 

Restriction in series-parallel combinations of capacitor elements 25/814... 

For-della connected capacitor units In (his case, it will establish a line-to-line fault with a heavy fault current. Protection by HRC fuses would be more appropriate than for a grounded star or using an MCCB. For series-parallel connected units I his is applicable in HT capacitor banks comprising a number of small units arranged in series and parallel combinations. The fault current in such cases for an isolated neutral can be expressed by... 

Reactor models consisting of series and parallel combinations of ideal reactors... 

The impedance data have been usually interpreted in terms of the Randles-type equivalent circuit, which consists of the parallel combination of the capacitance Zq of the ITIES and the faradaic impedances of the charge transfer reactions, with the solution resistance in series [15], cf. Fig. 6. While this is a convenient model in many cases, its limitations have to be always considered. First, it is necessary to justify the validity of the basic model assumption that the charging and faradaic currents are additive. Second, the conditions have to be analyzed, under which the measured impedance of the electrochemical cell can represent the impedance of the ITIES. 

The insertion is monopolar when the electrode functions exclusively as either the anode or the cathode and in this case it is connected with one of the poles of the electric source as shown in Figure 6.22 (a-f). Since the voltage for a single cell is very small (of the order of one to a few volts) several cells are usually connected in series and parallel combinations such that the overall potential drop corresponds to the available direct current power source. With bipolar insertions, however, there are a number of electrodes in each cell which function as anodes on one side and as cathodes on the other apart from the end electrodes, these are not directly connected to the electric source. 

In order to achieve increases in production capacity or to obtain higher conversion levels, it may be necessary to provide additional reactor volume through the use of various series-parallel combinations of reactors. 

This section indicates a few useful generalizations that are pertinent in considerations of isothermal series and parallel combinations of ideal plug flow and stirred tank reactors. 

Parallel combinations are governed by the general principle enunciated in Section 8.2.3. 

For series-parallel combinations of reactions a number of possible situations can arise. Two general guidelines are useful to keep in mind (11). First, if one has two undesirable products being formed in parallel with a desired species or with an intermediate product that can subsequently react to form the desired species... 

The piping and valves may be arranged to enable two centrifugal pumps to be operated either in series or in parallel. For two identical pumps, series operation gives a total head of 2Ah at a capacity Q and parallel operation gives a capacity of 2Q at a total head Ah. The efficiency of either the series or parallel combination is practically the same as for a single pump. 

At high frequencies, a semicircle is expected as a result of a parallel combination of R and Cg. At low frequencies a Warburg impedance may be found as part of the interfacial impedance. In some cases it may dominate the interfacial impedance as in Fig. 10.13(a), in which case only the diffusion coefficient of the salt will be determinable. It should be noted that, in the absence of a supporting electrolyte, the electroactive species, in this case Li, cannot diffuse independently of the anions. 

The relationship between the fractional surface coverage 9 and the double-layer capacitance C may be better understood in terms of the following model. The doublelayer capacitance at the electrode in the presence of adsorption can be viewed as consisting of two capacitors connected in parallel. One capacitor corresponds to the electrode areas that are unoccupied (free) and the other to the electrode areas that are occupied (covered) with adsorbate (13-15). These two condenser-capacitors have different dielectrics and thus different capacitances. The capacitance of a parallel combination of capacitors is equal to the sum of the individual capacitances. 

In this chapter we treat parallel reactions. In the next chapter we treat series reactions as well as all sorts of series-parallel combinations. 

Here co is the angular frequency and j = v/-T. For the parallel combination we write ... 

A similar analysis can be performed for the series combination, starting from the parallel combination. The resulting formulas are as follows. 

A parallel combination of comb filters with incommensurate delays is also a useful structure, because the resulting frequency response contains peaks contributed by all of the individual comb filters. Moreover, the combined echo density is the sum of the individual densities. Thus, we can theoretically obtain arbitrary density of frequency peaks and time echoes by combining a sufficient number of comb filters in parallel. 

Bridge measurements provide the most direct way to compare an unknown impedance with known standard impedances. The impedance may be a pure resistance, capacitance, or inductance, or may be represented by some series or parallel combination. The DC Wheatstone bridge95 provides a simple and... 

AC bridge measurements provide only an absolute impedance and phase shift, so there is no way to distinguish between either a series or parallel R-C combination by use of a pure sinusoidal waveform. Thus the series R-C combination of the cell may be matched by the series combination shown in Figure 6.24b or the parallel combination of the Wien bridge shown in Figure 6.24c. Either an oscilloscope or phase-angle voltmeter100 are recommended as null indicators because they allow both the phase shift and the imbalance potential to be nulled. 

It might seem more convenient to eliminate the calculation by employing a bridge with a series R-C balancing arm as in Figure 6.246. However, the parallel combination is used more frequently because the parallel capacitance required to compensate a series capacitance of 100 /iF at 1000 Hz with a resistance Rs - 1000 0 is only about 300 pF. Small capacitances can be obtained with high accuracy and less frequency dependence (and less cost) than large ones. 

When an electrode process involves several steps, sometimes a succession of semi-circles side by side is obtained, corresponding to RC parallel combinations in series and with different RC time constants, from which it is possible to deduce the corresponding parameters. 

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