If you connect a 12-volt battery to a 4-ohm lamp, 3 amps of current will flow through the circuit by Ohm’s Law, V=IR. Power = VI = 36 watts will be dissipated by the lamp. If you add a 2-ohm resistor in series with the lamp, the resistances add to 6 ohms, the current is 2 amps and the circuit thus dissipates 24 watts. The voltage across the resistor is 4 volts so it dissipates 8 watts and the lamp gets 8 volts and dissipates 16.

What if you had a gadget with a resistance of *negative* 2 ohms? Let’s replace the resistor with it and see what happens: total resistance 4-2=2 ohms, current 6 amps, voltage across the lamp 24 volts, voltage across the resistor **minus** 12 volts. The lamp is dissipating 144 watts, of which the battery at 12V*6A is only supplying 72 — the resistor is supplying, rather than dissipating, the other 72.

It’s fairly easy to create a circuit that exhibits negative resistance using op amps:

… but why would you want to?

After all, the energy from the op amp isn’t free; it draws its power from somewhere. But suppose you had a circuit element that had some source of energy, say, it was photovoltaic and sat in the sunlight. Then acting like a negative resistance might be a useful way to act in a circuit.

For example, a sheet of resistive material when considered as a 2-D shape has a very simple and regular resistive behavior: any square shape of it has the same resistance, no matter what size. (Resistivity of layers in VLSI is measured in “ohms per square”, for example, a parameter dependent on the material but not the size.) Essentially the wider the path, the lower the resistance, and the longer, the higher, so in any square, they cancel.

Now suppose you had nanofabricated modules, say 10 microns in diameter, dispersed as an emulsion in a fluid, which you then put in an ordinary paint sprayer and applied to the roof of your house. The incalculably complex network of nanomodule touching nanomodule across the house adds up to the nice even continuous sheet approximation and you just count squares from electrode to electrode.

Suppose your house load (all your appliances, in parallel) is 10 ohms and you’d like to match it with a -10 ohm solar sheet. Your roof is 20 feet wide and 40 feet long — 2 squares — so get -5-ohm-per-square paint and put electrodes at each end. If the hardware store only carries -20-ohm-per-square paint, put the electrodes along the sides so the squares are in parallel.

You can’t, however, put the roof in series with your house load as in the lamp example above. Consider what happens if the negative resistance just matches the load: 4 ohm lamp, -4 ohm resistor, total resistance 0, current at 12V infinity. (It’s trying to simulate a superconductor.) Woops!

What you do is what any sane electrician would have done in the first place, which is put the roof in parallel with the house load. Then if the resistances match exactly, the result is infinite rather than 0 resistance, and 0 rather than infinite current (to be drawn from the grid). Which is roughly how solar panels work anyway. (I’m pretending it’s DC, but the AC case is similar if a bit more, um, complex.)

Footnote: This only scratches the surface of solar paint. For example, loops of negative resistance would act to amplify magnetically induced eddy currents, wasting power. It would be an amplifying mirror for electromagnetic radiation. So in practice, you’d have to engineer and tune a whole range of electromagnetic properties at many frequencies.

AnonymousMay 22, 2009 at 3:20 pmDrift-diffusion balance explains `negative resistance’ of material

Electronics Times, July 27, 1998, by Nadya Anscombe

Researchers in the US have developed a carbon fibre composite material which exhibits `negative resistance’ – a phenomenon which essentially means electrons appear to flow the wrong way.

Professor Deborah Chung from the University of Buffalo says that combining the material with conventional composite structures, which have high positive resistance, will produce a material that is a superconductor at room temperature.

The research is aimed at giving electronic function to composite structures used in the aerospace and automotive industries. These materials, which consist of layers of carbon fibres bound together with epoxy resin, normally exhibit large resistance in a direction perpendicular to the carbon fibres.

While carbon fibres themselves are electrically conducting, the polymer matrix is an insulator. But resistance is never infinite because there will always be some contact between fibres of adjacent laminae.

Prof Chung found that, if the composite was made with a curing pressure of above 1.4MPa (200psi), negative resistance could be observed at the junctions where the carbon fibre layers are in contact.

Prof Chung describes her findings as “surprising”, saying that these interfaces are geometrically very complex and the reason for negative resistance is unclear. Energy is needed to get the electrons to jump from one lamina to another but its source is unknown.

One suggested mechanism is based on an imbalance of drifting and diffusing electrons. When a voltage is applied, electrons drift between adjacent lamina which are not electrically connected; electrons then diffuse back to the bottom lamina at the short-circuited regions of the interface.

This diffusion current seems to overshadow the drift current, giving the impression of electrons flowing the wrong way. Prof Chung is now working on the theory that this phenomenon “may be driven by the applied current and the entropy-driven backflow of electrons”.

The discovery was made accidentally, while examining the electrical behaviour of carbon composites as a way of improving damage detection. Prof Chung says the research could result in `smart’ aircraft parts which sense their own strain or automotive parts capable of storing huge amounts of power.

Like silicon, carbon fibres can be doped to be n and p-type semiconductors. The research team has already made np junctions (diodes) and is working on making transistors.

“This is a whole new level of `smartness’ in materials,” she said. “For example, using composite structures as electronic components means electronic capabilities could be spread over a much larger surface area, eliminating the problem of heat dissipation.”

It also means aircraft parts could be made without the need to embed sensors, thus improving mechanical properties.

AnonymousMay 24, 2009 at 7:23 pm“Suppose your house load (all your appliances, in parallel) is 10 ohms and you’d like to match it with a -10 ohm solar sheet. Your roof is 20 feet wide and 40 feet long — 2 squares — so get -5-ohm-per-square paint and put electrodes at each end. If the hardware store only carries -20-ohm-per-square paint, put the electrodes along the sides so the squares are in parallel.”

Ummm, wait just a second here. Just because your hypotech paint could be rated in negative-x-ohms-per-square doesn’t show that a given swath could deliver the needed /power/. If my house is a purely resistive 10 ohms and runs on 120 V RMS, then the current needed will be 12 A. I^2R is 1440 W. Your “per-square” analysis would make it appear that a postage stamp of the stuff would work just as well as the 20 by 40 array.

AnonymousMay 28, 2009 at 9:04 pmSmartness of materials…. and their effects can teach humans to become morally smart to materialize the dream of immortal life which is partly the objective of nanotechnology( longevity of human life span)