One application for electronics that has gained a lot of attention over the past several years is in so-called"bio-molecule" detection. The idea is to build a system that detects the presence of specific moleculesand/or cells (e.g. specific viruses, proteins, etc.) in a biological sample; if this detection can be performedautomatically and using relatively low-cost components, it can have a dramatic impact on a number of areassuch as medical diagnosis, drug development, DNA sequencing, etc.In this problem, we'll look at how some of the techniques we learned about in the touchscreen module canbe applied to realize a hypothetical bio-molecule detector. (Real bio-molecule detection systems involvequite a bit more complexity than what we'll include here, but in many designs the same basic principlesapply.)As shown in Figure 3, the detector works by flowing a liquid that may or may not contain the biomoleculesthrough a region in the device that has electrodes on the top and bottom of the liquid channel. The electrodes(EI/E2 in Figure 3) are chemically "functionalized" (using e.g. some appropriately designed antibodies), sothat if the specific bio-molecule of interest is present in the fluid sample, one or more of the molecules willget physically trapped between the two electrodes (bottom right of Figure 3). After all of the fluid has beencleared out of the device (i.e., so that if there are no bio-molecules present, there is only air in between theTon ViewFluidinletFluidoutletDetectionElectrodesSide ViewmoleculesSide View(no molecules)(molecules present)Zoomed in malecule(side view)Figure 3: Bio-molecule detector.two electrodes EI/E2), we can then figure out whether or not one or more bio-molecules were trapped bymeasuring the resistance between the two electrodes.(a) Let's first assume that we want to detect the presence of a bio-molecule by measuring resistance. Ifno bio-molecule is present, what should be the resistance between E1/E2? As shown in Figure 3, ifcach bio-molecule is a cylinder with diameter d = 10nm, height h = 100nm, and has a resistivityp = 100u2m, what would be the resistance between El and E2 if only a single bio-molecule has beentrapped? Note that you can assume that the trapped molecule is exactly vertically oriented when it istrapped – i.c., the top and bottom faces of the molecule are both aligned with surfaces of the electrodes.(b) Using the same numbers for d, h, and p as part (a), as a function of the number of trapped bio-molecules Nuokecules. what is the resistance between El and E2? (Note that you can assume thatNmolecules is small enough that all of the molecules fit within the electrode area and that all of themolecules are still trapped in an exactly vertical orientation.)(e) Given your answers to parts (a) and (b), design a circuit that will output a voltage greater than 2.5 V ifmore than 5 molecules are trapped.

Question

One application for electronics that has gained a lot of attention over the past several years is in so-called&#34;bio-molecule&#34; detection. The idea is to build a system that detects the presence of specific moleculesand/or cells (e.g. specific viruses, proteins, etc.) in a biological sample; if this detection can be performedautomatically and using relatively low-cost components, it can have a dramatic impact on a number of areassuch as medical diagnosis, drug development, DNA sequencing, etc.In this problem, we'll look at how some of the techniques we learned about in the touchscreen module canbe applied to realize a hypothetical bio-molecule detector. (Real bio-molecule detection systems involvequite a bit more complexity than what we'll include here, but in many designs the same basic principlesapply.)As shown in Figure 3, the detector works by flowing a liquid that may or may not contain the biomoleculesthrough a region in the device that has electrodes on the top and bottom of the liquid channel. The electrodes(EI/E2 in Figure 3) are chemically &#34;functionalized&#34; (using e.g. some appropriately designed antibodies), sothat if the specific bio-molecule of interest is present in the fluid sample, one or more of the molecules willget physically trapped between the two electrodes (bottom right of Figure 3). After all of the fluid has beencleared out of the device (i.e., so that if there are no bio-molecules present, there is only air in between theTon ViewFluidinletFluidoutletDetectionElectrodesSide ViewmoleculesSide View(no molecules)(molecules present)Zoomed in malecule(side view)Figure 3: Bio-molecule detector.two electrodes EI/E2), we can then figure out whether or not one or more bio-molecules were trapped bymeasuring the resistance between the two electrodes.(a) Let's first assume that we want to detect the presence of a bio-molecule by measuring resistance. Ifno bio-molecule is present, what should be the resistance between E1/E2? As shown in Figure 3, ifcach bio-molecule is a cylinder with diameter d = 10nm, height h = 100nm, and has a resistivityp = 100u2m, what would be the resistance between El and E2 if only a single bio-molecule has beentrapped? Note that you can assume that the trapped molecule is exactly vertically oriented when it istrapped – i.c., the top and bottom faces of the molecule are both aligned with surfaces of the electrodes.(b) Using the same numbers for d, h, and p as part (a), as a function of the number of trapped bio-molecules Nuokecules. what is the resistance between El and E2? (Note that you can assume thatNmolecules is small enough that all of the molecules fit within the electrode area and that all of themolecules are still trapped in an exactly vertical orientation.)(e) Given your answers to parts (a) and (b), design a circuit that will output a voltage greater than 2.5 V ifmore than 5 molecules are trapped.

Accepted Answer

As seen in the diagram, there is resistance between E1 and E2 and is given by the equivalent…