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I was having a conversation last week with a student about negative resistances (in an electronics context). These are just as they sound – to send a current from terminal A to terminal B you have to apply a higher potential to terminal B than terminal A.  Sounds backwards?  Yes – it is. That’s why the resistance is negative.

It’s not possible to get a negative resistance with purely passive components. We can see that from thermodynamics. A normal (positive) resistor puts out heat to the surroundings – voltage times current gives us the power dissipated.  A negative resistor would need to suck in heat and turn it to electrical energy. For example, if you connected a negative resistor to a battery, the current would flow backwards through the battery – i.e. charge it up. The energy would come from the surroundings, being sucked in by the negative resistor.  It would be a nice solution to global warming, but unfortunately the second law of thermodynamics says you can’t do it.

So how can you get a negative resistance?  You can use active components – e.g. operational amplifiers, that have a power source. There are a few circuits that effectively produce a negative resistance, for example this one.  To put a positive current into the circuit, you have to apply a negative potential difference.   If I put a battery across the terminals, it would recharge. Where does the energy come from, if it can’t come from the surroundings?  The operational amplifier needs its own power supply  – that is, it is not a passive component. The second law of thermodynamics can rest easy.

There are lots of neat applications – perhaps the most obvious is simply ’cancelling’ unwanted positive resistances.  Related to negative resistance, but not the same thing, is negative differential resistance. This is something that can be made from a purely passive component, for example in a tunnel diode. Here, if you plot a graph of the current through the diode (y-axis) against the voltage across the diode (x-axis) there is a region where the gradient is negative. That is, increasing the voltage causes less current to flow.  However, this doesn’t break the second law of thermodynamics since the current is still positive for a positive voltage. In calculus terms, dV/dI is negative (in a small region), though V/I remains positive.  Tunnel diodes can be used in oscillators.

There are lots of cool things you can do with Operational Amplifiers, negative resistances are just one. Have a go at making a negative resistance, and see what you can do with it.