TWO RESISTORS

Ordinary resistors are only available in a few standard sizes, which have been agreed upon by the Radio-Electronics-Television Manufacturer s Association (RETMA). These sizes are various decades, such as 1, 10, 100, 1000, 10000, etc., multiplied by any number chosen from  

The series listed above consists of multiples of the sixth root of ten (10 or ),which is 1.467. Multiplying that times itself six times yields a number close to 10. This allows us to divide a decade (that is, a group of resistances increasing by a factor of ten, like 100 to 1000) into six small steps, spaced out evenly in a logarithmic manner (that is, like 100, 150, 220, 330, 470, 680, and 1000, or in the next decade, 1000, 1500, 2200, and so on). 

The fourth ring (not near an end of the resistor) represents the tolerance (accuracy). Gold = plus or minus 5% (usually written i 5%), and silver = plus or minus 10%, and no colored ring there means plus or minus 20%. 

If a water pump system is operated at the same pressure (height of water level visible in the glass tube) as was used in the previous chapter, but this time there are two faucets instead of one, then more water would be expected to flow. This is illustrated in Fig. 3.1. If each of the new faucets is open to the 

The reader can easily imagine an electric circuit where a battery is analogous to the water pump, and two resistors are analogous to the valves shown above. Of course, the flow of electric current would be double that of the case where there is only a single resistor, very similar to the behavior of the water analog. If the voltage is the same but the current is doubled in the two-resistor case, then Ohm s law tells us that the total resistance in the two-resistor case must be half that of the one-resistor case. This is quite intuitive and simple, when both resistors are equal. 

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Multiple output sensing is done by using two resistors in the top of the voltage sensing resistor divider. The top-end of eaeh resistor goes to a different positive output voltage as seen in Figure 3 4. 

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. 

In order to improve the slope compensation circuitry that depends upon a resistor to ground all the time, I will split this resistor between the secondary winding of the current transformer and after the rectifiers. I will double the value of the two resistors (150 ohms each), so that when the diodes are conducting, the net value is the same. 

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

A passive lead network (using two resistors and one eapaeitor) has a transfer fune-tion of the form... 

Before we go deeper into the high-frequency aspects, let us examine what happens if we ascribe even a simple DC resistance to a trace. As an example, we pick the case of a simple voltage divider, as shown in Figure 2-1. This combination of two resistors is used to set the output voltage, and is probably the most ubiquitous part of any voltage regulator—whether... 

When designing a PCB for a switcher IC, try to plan ahead and leave the option of moving back from a fixed-voltage part to an adjustable-voltage part (leave room for two resistors). That is a likely retreat in the face of various problems you may encounter. 

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,... 

Calculate the voltage drops across the two resistors based on the current value computed in step 8 and the individual resistance values. Comment on whether these voltage drops agree with what was measured in step 9. 

Figure 1.4. Adsorption analogy to two resistors in a series adsorption of an organic compound to sediment.

The astable operation of the UA555 as an oscillator has a duty cycle and free running frequency, which are both precisely controlled with two external capacitors and two resistors. The circuit is shown in Fig. 8.1. 

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 j/V curve is substantially modified by these two resistors, since the series resistor consumes the voltage V(RS) = jRs, whereas the shunt adds the current density jp = (V — jRs)/Rv to the output current density. 

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. 

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... 

Although the values of tlie two resistors are easily discerned, there is no region in which the circuit behaves as a pure capacitor. The slope never reaches a value of - 1, and (p never even comes close to - 90°, which one would have for a pure capacitor. 

The resistance of an element with a particle included, 57 , is that of two resistors 5/ , 57 2 in parallel... 

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 ... 

The contact resistance enters the equations of OFET operation because the source-drain circuit is represented by two resistors connected in series — the contact... 

Schufle et al. [29,30] and Rutgers and de Smet [31] have evaluated the total conductance of solutions contained in capillaries, to assess the excess surface conductance due to the presence of the electrical double layer. The model treats the system as two resistors in parallel one comprising a bulk resistance afforded by an homogeneous cylinder of electrolyte and the other is attributable to the ion excess in the double layer at the capillary wall. A formula for the total resistance, R, is given... 

I or ihe special ease of two resistors in irarallel. liquation 2-1.4 can be solved to give... 

In oiher words, for two parallel resistors, the fraction of the current in one resistor is just ihe ratio of the resistance of the second resistor to the sum of the resistances of the two resistors. The equations lor 1,11, and ate often called the ciirmil-.y>Ii iii y vipnitiims. 

Thus. Ihc output voltage i is the input vollage i, multiplied by the ratio of two resistors, and of opposite polarity. If Ihe two resistors are precision resistors, the amplilier closed-loop gain. R,IR can be made quite accurate. I or example, if K were KK) kll and R, were 10 kf . Ihc gain would be 1(1 and v - - 10 x i-,. Note that the accuracy of the gain depends on how accurately ihe two resistances are known and not on the open-loop gain, A. of the operational amplilier. 

The following schematic diagram shows lhat ihc niea-surement circuit can be considered as a voltage source and two resistors in series the source resistance R, and the internal resistance of the measuring device R i. 

This equation describes the instantaneous flow rate through a filter it is analogous to Ohm s law for two resistors in series, so the fj, Ax/k terms are called the cake resistance and the cloth resistance. 

A version of the multianode PMT uses a system of crossed wires as the anode [297]. In principle, individual wires could be connected to a TCSPC device via a router as in the case of the multianode PMT. Another way to obtain the X-Y information is to connect the wires via two resistor chains, as shown in Fig. 6.5, left. The spatial coordinates of the photons are then determined by measuring the pulse amplitudes at the ends of the resistor chains. 

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