by CafeT, published
Update: Using an Archimedean spiral approximation, I think this would be about 1.33 ohms in copper, 86.9 ohms in nichrome, 17.4 ohms in lead, 1.65 megaohms in sea water. I imagine this could be raised quite significantly if one could print the resistor in layers along the Z axis (at the same resolution and trace size, 10 times per millimeter).
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In electrophysiology and astronomy it is helpful to reliably produce resistors in the range 20 meg ohms to 100 gig ohms. For example a TL084 fet input amp (input impedance 10^15 ohms, output impedance ~75 ohms), used as a voltage follower will easily track the millivolt voltages of nerve fibers or heart beat, but the wall resistance for a cell wall is often around 5 to 15 meg ohms, 5 meg can be used as a load resistor or to measure current flow. (e.g. See Scientific American article ~1970 for tracking Daphnia heart beat in a jar of swamp water). Whereas, a 500 meg resistor can bleed capacitative charge while reducing noise. Similarly, a small CdS or indium telluride sensor can reliably sense the light from a single star but the impedance change, the resistance changes are 10^9 to 10^12 ohms. A battery in series with a 10gig resistor and sensor can be used to create a voltage divider, An EEG 4 quad sensor using TL084 or equiv. can sense that voltage, and the result can be used for scope alignment or for a star or satellite tracker.
DuPont has inks that could be used to print resistors - years ago we did thick film circuits. Resistors were typically screen printed, fired and then trimmed with laser. The same applied to conducting strips. Soldering was achieved by screen printing solder paste on the contact points. Components was either electronically or manually (prototyping) placed - the beauty was the placement did not have to be absolutely accurate as the solder will help to pull it in position on the tabs as soon as that was heated.
Warning on the above - it is also an effective coil.....
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