Resistor in series

Another faetor is the rated breakdown voltage of resistors. For a one-quarter watt resistor, the rated breakdown voltage is 250 VDC. The one-half watt resistor is 350 VDC. To design safely, two resistors in series should be used on all branehes that are eonneeted to the input line in off-line eonverters. 

The total resistanee of the eolleetor resistors (two resistors in series for voltage breakdown reasons) should have an approximate resistanee of... 

If we plaee two 8.2 K ohm, 5W resistors in series, we ean spit the dissipation between two resistors and also guarantee that the resistors will not reaeh their breakdown voltage. 

Onee again, plaee two resistors in series to avoid resistor voltage breakdown problems (250 V for 1/4 W resistors). So two 240K, 1/4 W resistors will be used. 

Make this two resistors in series eaeh with a value of 910Kohms. 

Make this resistor a IMohm and a 910Kohm resistor in series, eaeh with a 1/2 W rating. 

It was observed that with a linear circuit and in the absence of any source of energy (except probably the residual charges in condensers) the circuit becomes self-excited and builds up the voltage indefinitely until the insulation is punctured, which is in accordance with (6-138). In the second experiment these physicists inserted a nonlinear resistor in series with the circuit and obtained a stable oscillation with fixed amplitude and phase, as follows from the analysis of the differential equation (6-127). 

In DC-DC converters, we can somewhat slow the turn-on of Fets if we insert a small resistor (10 to 20Q. typically) in series with the decoupling capacitor of their respective driver stages. For example, a small resistor can be placed in series with the bootstrap capacitor of the third-generation switcher family I used to cover. That helped with almost 10 to 20% of customers, but somehow this trick didn t find its way into the applications information section of their datasheet. If the Fets are external, we can try a small resistor in series with the Gate, but this affects both the turn-on and turnoff (with such low threshold voltages, a diode in parallel to the resistor will not do anything). 

So, if you can access the gates of the Fets, try putting in small resistors in series with them. If it is a switcher IC (with no access to the gates), try inserting a small resistor in series with the decoupling capacitor of the driver supply (usually a 0.1 pF capacitor attached to the Vdd pin and/or the bootstrap pin). Better still, pick an IC with less aggressive drive to start with. Because otherwise it will commit suicide sooner or later. 

Next, measure your resistors connected two at a time in series. This means that two of the resistors are connected end to end. When two resistors are connected in this fashion, the total resistance is the sum of the two. To do this, use the socket board and insert the wire ends of one resistor into sockets FI and F5 (as in step 5), for example, so that the ends are not connected internally. Then insert the wire ends of the other resistor into sockets G5 and G9, for example. Since G5 and F5 are connected internally, this connects both resistors in series. Now measure the total resistance by touching the lead tips of the multimeter to sockets HI and H9. Record the individual values of the two resistors, the sum of the two, and the measured value of the sum in another table (four columns) in your notebook. Repeat with several different combinations. Comment on the agreement (or lack thereof) between the calculated and measured values. 

Construct a complete circuit with a battery and two resistors in series. To do this, choose the two resistors you want to use and connect them in series on the socket board, as in step 6. Then,... 

The electrolyte is very conductive. In my example of 7 separate containers wired in series, there s no charge applied to the middle ones either because they are in series If you wire 7 resistors in series you have 1/7th of the total voltage across each resistor. I wanted to get about 2V dc per cell, and with 7 cells you can use a 14V dc power supply (for example a battery charger). You could scale up to any number of plates, but the voltage across the stack would be higher. If 7 cells produce 7 units of gas with a given current then 100 cells would produce 100 units of gas with the same current, but the voltage across the whole stack would need to be about 2V multiplied by the number of cells. Thus the power consumption increases approximately linearly with the number of plates. 

The ideas of reaction steps in series and rate-limiting steps can be best understood by the idea of resistors in series. If a voltage V is applied across a resistor with resistance R, the current flow 1 is given by Ohm s Law,... 

For three resistors in series, the current through each resistor is identical so that... 

For resistors in parallel, the current (flux) branches between paths while the voltage (concentration at each end) is constant. The electrical analogy of resistors in series and parallel allows one to solve these problems quite simply. 

The actual SPICE model of this circuit is shown in Fig. 10.2. Note that there are two resistors in series with each of the capacitors, Rl and R2. These resistors model the approximate equivalent series resistance (ESR) of the tantalum capacitors in the circuit at the switching frequency. 

The voltage becomes distributed just as in the case of a potential, E, applied to three resistors in series ... 

Resistors in series behave in the same manner as batteries in series. The equivalent resistance is simply the sum of the individual resistances. Figure 10.7 illustrates this point. 

Figure 3.5 Schematic representations of typical electrochemical quartz crystal microbalance equipment (a) using a Wenking potentiostat in which the working electrode is at hard ground (b) using a conventional potentiostat in which the current is measured by the voltage drop across a 1 kS2 resistor in series with the counter electrode...

P and I are shown as functions of U in Fig. 4.16 and R is shown as a function of U in Fig. 4.17. The curves represent equilibrium conditions, and it is evident that no equilibrium can exist above a certain maintained maximum voltage. If a higher maintained voltage is applied, the current will go on rising indefinitely until the accompanying high temperature destroys the unit. In practice there must always be a temperature-insensitive resistor in series with a thermistor if sufficient power to raise its temperature appreciably is to be applied. 

Resistors in series Rlr R2, R3,..have an overall resistance R that is the sum of the individual resistances ... 

Electric circuits or networks can be analyzed using both Ohm s law and KirchhofFs laws. For a circuit of resistors in series, as shown in Figure 2.6, the current flow in each resistor is the same (IR). 

Finally, the overall impedance between the source fy and the sink E2 is represented simply by three resistors in series and is thus given by... 

Dry deposition processes are best understood by considering a resistance analogue. In direct analogy with electrical resistance theory, the major resistances to deposition are represented by three resistors in series. Considering the resistances in sequence, starting well above the ground, these are as follows ... 

A resistor in series will help, but will reduce the effectiveness of the filter. A capacitor network is also ineffective if the transient has high energy in either polarity. Filters can become expensive and must be very carefully designed. 

We will analyze the electrical circuit presented in Figure 8-5 first in terms of resistances and then in terms of conductances. We begin by noting that the resistances and occur in series. The total resistance of a group of resistors in series, rseties is the sum of the individual resistances ... 

The result is a semicircle having a radius equal to R 2, with its center on the x axis and displaced from the origin of coordinates by R + RJ2. Each point on the semicircle in Fig. lOG represents a measurement at a given frequency. At very high frequencies, the fara-daic resistance is effectively shorted out by the double-layer capacitance, leaving the solution resistance in series as the only measured quantity. At very low frequency the opposite occurs, namely, the capacitive impedance becomes very high and one measures the sum of the two resistors in series. 

For any method to be used prudently, it must be remembered that as a rule, the interphase consists of a resistor in series with a parallel combination of a capacitor and a resistor. If both resistances are high, one should try to conduct measurements at low frequencies. If both are low, the experiment should be conducted at high frequency. 

In the absence of mass transport limitations, the local current density at a given potential is determined by the sum of two resistors in series the faradaic resistance and the solution resistance. For values of Wa much less than unity the solution resistance is dominant and the current distributions depends primarily on geometry. This is the realm of primary current distribution. For Wa much greater than unity the faradaic resistance is predominant and secondary current distribution is... 

The potential drops were measured across the sample rod and a standard resistor in series with a sensitive VTVM (vacuum tube volt meter) while the wave form was monitored with an oscilloscope. Two samples of composition Lal2.oo- o.oi were measured from 77° to 344° and 186° to 408°K., respectively, without irreversible temperature effects. One sample of composition Cel2.o7 was studied from 153° to 300 °K., but satisfactory Prl2 samples could not be obtained. Because of phase relationships and the relatively high resistivity found, Lal2.42 was studied as a pellet formed with a KBr press using a VTVM in the dry box. The results from one sample to another were somewhat erratic, partly because of extreme susceptibility to oxidation, but were sufficient to characterize the compound as salt-like as opposed to metallic. 

Example 11.5 Diffusion Impedances in Series If, as is shown in eqmtion (4.23), the impedance corresponding to two resistors in series is equal to the sum of the resistances, why is it incorrect to treat diffusion through two layers by adding two diffusion impedances ... 

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