# How do superconductors avoid breaking Kirchoff's Voltage Law?

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):

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?

Electrical Engineering Asked on November 21, 2021

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.

Answered by user_1818839 on November 21, 2021

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.

Answered by Spehro Pefhany on November 21, 2021

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