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So, let's imagine that you've got a superconductive voltage source (e.g. a wind turbine) hooked up to a loop of superconductive wire to form a circuit. Kirchoff's Voltage Law states that the sum of electrical potential differences around a circuit must be equal to zero; however, in this scenario, you've got a voltage source hooked up to a circuit with no apparent voltage drops. In analysis of ideal circuits, this is where you add in parasitic resistance, but if everything in the circuit is composed of superconductors, their resistance would be zero, right?

Here's an image of the circuit (I apologize for low-quality because I made it in MS Paint because I don't have any professional circuit-drafting software, and I can't find the symbols used to designate things as being superconductors):

circuit

Obviously, there has to be something screwy going on here; where is the voltage dropped? Is there some sort of exotic property of superconducting materials that comes into play in these situations?

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  • \$\begingroup\$ Draw out the circuit you are envisioning and add it to your question. So far nothing sounds problematic. \$\endgroup\$
    – relayman357
    Commented Jul 22, 2020 at 8:48
  • \$\begingroup\$ Superconductors just don't obey Ohms law. When Ohm posted his laws we hadn't discovered superconductors yet so his laws cannot be applied. \$\endgroup\$
    – Helena Wells
    Commented Jul 22, 2020 at 8:53
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    \$\begingroup\$ You need to be very careful in your definition of "superconducting voltage source". If you're thinking of a coil of superconductor plus a moving magnetic field, that's a superconducting current source. \$\endgroup\$
    – pjc50
    Commented Jul 22, 2020 at 8:53
  • \$\begingroup\$ the only difference here is that the conductor is closer to the ideal models, where KVL and KCL work anyway. In your thought experiment the entire loop will be at 0V, and all the voltage drop will be the voltage source output impedance. Since that thing isn't usually very large, you'll get a ton of current there, but still limited. Although in this case probably your voltage source would explode from the amount of current. That is, if you just short your turbine to ground with the superconductor, which is how I understood your question \$\endgroup\$
    – Ilya
    Commented Jul 22, 2020 at 8:54
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    \$\begingroup\$ Infinite current would flow! The Universe would blow up! Dogs and cats would start living together! Or... physics.stackexchange.com/questions/231357/… \$\endgroup\$
    – Bruce Abbott
    Commented Jul 22, 2020 at 8:55

2 Answers 2

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The wind turbine will simply stall.

To generate any voltage at all, it must supply infinite current, which requires infinite torque, and the wind is never quite that strong.

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  • \$\begingroup\$ Good point! You know that experiment where a magnet gets stuck to a superconductor? You are creating that inside your turbine. \$\endgroup\$
    – Criticizing Israel not allowed
    Commented Jul 22, 2020 at 9:48
  • \$\begingroup\$ I don't see why it would stall. The magnetic field will be pushed into the air gap and it will get harder to turn. \$\endgroup\$
    – Spehro 'speff' Pefhany
    Commented Jul 22, 2020 at 9:51
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In the case of a wind turbine wound from superconducting wire, the current induced in the wire would create a magnetic field opposing the motion of the blades. The voltage would remain at zero* but there would be current flowing. That's ignoring the inductance of the loop of superconducting wire, which can have voltage across it if the current is changing just like any other inductance.

KVL does not apply to inductors if you think of them as pieces of wire, only as lumped elements, and even a piece of straight wire a few mm long has some inductance (maybe 1nH).

*provided the current was less than Jc the critical current density of the weakest part of the circuit.

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  • \$\begingroup\$ KVL does apply to inductors when you treat them as discrete circuit elements. \$\endgroup\$
    – Criticizing Israel not allowed
    Commented Jul 22, 2020 at 9:47
  • \$\begingroup\$ @user253751 Yes, clarified. \$\endgroup\$
    – Spehro 'speff' Pefhany
    Commented Jul 22, 2020 at 9:50

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