Series and Parallel Connections

When reactors are connected in series, the output from one serves as the input for the other. For reactors in series, 

The design equations for reactor 1 are solved and used as the input to reactor 2. 

Example 4.8 Find the yield for a first-order reaction in a composite reactor that consists of a CSTR followed by a piston flow reactor. Assume that the mean residence time is ij in the CSTR and ti in the piston flow reactor. 

Solution The exit concentration from the perfect mixer is 

Using Equation (4.14) to combine these results gives 

Compare the ontlet concentration of the composite reactor to that from a single CSTR and to a PFR having the same mean residence time  

---

Semiconductor solar cells are low voltage power sources (<1 V) and therefore are used in series and parallel connected batteries. For this reason, the term semiconductor solar battery is more appropriate than the often used term semiconductor solar cell. 

In an electrical circuit resistors may be connected in series, in parallel, or in various combinations of series and parallel connections. 

Formula (81a) is nothing but an expression for the conductance of a composite circuit with series and parallel connections of its elements whose conductance is llJp )/ RT/nF). 

Series and Parallel Connection of Capacitors Construction of Practical Capacitors Standard Values and Tolerances of Discrete Capacitors Typical Parameters and Characteristics of Discrete Capacitors Capacitor Impedance Characteristic... 

The formulas for series and parallel connection of capacitors can be obtained from the general consideration of series and parallel connection of impedances. For series connection... 

All strains and stresses ate supposed to be uniform and homogeneous in the whole volume of each particle in all phases. Mutual interactions are realized at the phase interfaces. Strains and stresses ate distributed in a different manner for the different components as well as for the different volume distributions of the phases. Let us demonstrate the approximation for series and parallel connection of two phases (Fig. 7.25). In series connection, stress component along X3-ditection is the same in all phases, while the strain is different in the phases due to the different stiffness On the contraiy, strains ate the same in both phases in the direction perpendicular to the x3-axis, while the stresses are distributed differently in both phases. Assuming all interface conditions, following effective material properties could be calculated (similar method is applied also to the parallel connection of the elements)... 

However, the response to faults (especially multiple faults) differs significantly. The two Eqns. (16) and (18) are used to determine the cumulative reliability distribution for series and parallel connections. 

Different configurations consist of several levels series and parallel connections are considered and modelled using multi-state systems. The results show that even with the same number of elements in the same two dimensional arrangement, the selection of the best suitable configuration (as determined by the lateral connections) has a significant influence on the reliability of the HRA. 

Figure 2.13 Cross-sections of Westinghouse multi-cell module concept, showing the components of the ceils as well as series and parallel connection (1982).

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... 

Tlie reliability formulas for series and parallel systems can be used to obtain tlie reliability of a system lliat combines features of a series and a parallel system. Consider, for example, tlie system diagrammed in Fig. 20.2.1. Components A, B, C, and D have for llieir respective reliabilities 0.90, 0.80, 0.80, and 0.90. The system fails to operate if A fails, if B and C both fail, or if D fails. Component B and C constitute a parallel subsystem connected in series to components A and D. The reliability of the parallel subsystem is obtained by applying Eq. (20.2.2), which yields... 

Photovoltaic systems for specific applications are produced by connecting individual modules in series and parallel to provide the desired voltage and current (Figure 4). Each module is constructed of individual solar cells also connected in series and parallel. Modules are typically available in ratings from a few peak watts to 250 peak watts. 

We have considered two types of ideal flow reactor the piston flow reactor and the perfectly mixed CSTR. These two ideal types can be connected together in a variety of series and parallel arrangements to give composite reactors that are... 

PSB electrolytes are brought close together in the battery cells where they are separated by a polymer membrane that only allows Na ions to go through, producing about 1.5 V across the membrane. Cells are electrically connected in series and parallel to obtain the desired voltage and current levels. The net efficiency of this battery working at room temperature is about 75%. It has been verified in the laboratory and demonstrated at multi-kW scale in the UK [92]. 

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. 

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...

Strictly speaking, a single electrochemical power system is denoted a cell or element, whereas a series or parallel connection of cells is named a battery. The literature is confusing, as the terms fuel CELL and BATTERY are used independent of the number of cells described. 

In a typical electrowinning or electrorefining operation, the electrolytic cells are rectangular tanks, and each contains 20-50 electrode pairs. An additional anode is required in each cell to ensure deposition on both sides of each cathode. The electrodes are designed to rest on busbars that supply electricity. The busbars are situated outside the top of each tank, one for the anodes and another for the cathodes. Thus, the electrode pairs in each tank operate in parallel. In the tankhouse, the cells are arranged in sections with the banks of cells connected in series and parallel to obtain optimum use of the electrical power, while keeping the voltage to earth at any point at a low level that is not a risk to the personnel. 

Hybrid thermal vehicles are more expensive than traditional vehicles, because they include more than one energy source on board. However, there are some components of traditional vehicles which are not required for hybrid vehicles and can be made some savings. For instance, in the series conhguration there is no need for the gear box because the electric drive regulates the motor speed electronically, transmission is simplihed and differential is useless if the motors are directly connected to the wheels. The starter can be eliminated in both series and parallel conhguration since electric machines do not need any specihc devices to start. Many hybrid vehicles are currently on the market and this sector is growing rapidly worldwide. 

Figure 2.10 illustrates different types of inductive displacement sensor (a) self-inductance, (b) mutual inductance and (c) differential transformer. In most cases a mutual inductance system can be converted into a self-inductance system by series or parallel connections of the coils. The mutual inductance device (figure 2.10(b)) becomes a self-inductance device (figure 2.10(a)) when terminals b and c are connected. 

Fig. 5.4. Series connection (a) and parallel connection (b) of regions with different values of the transition temperature T (one-dimensional case). Along the x- and y-direction the regions are marked with the index i and j, respectively. (From Ref. [5.14].)...

The relation between unit, stage, and cascade is illustrated by Fig. 12.8. Each unit of this cascade might represent, for example, an electrolytic cell. The group of parallel-connected cells, each of which separates feed of composition zi into a partially enriched stream of composition yi and a partially depleted stream of composition, constitutes the fust stage of this cascade. The cascade is the entire group of series- and parallel-coimected cells. 

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 -... 

---