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Theoretically, shouldn't there be no current flowing through a short circuit?

Across the short circuit, the voltage is 0, and the resistance is ideally 0 as well.

So how does it make sense for any current to pass through?

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theoretically, the answer is no. here is a way to visualize it:

Start off with a voltage source of V volts connected to a resistance of R ohms. this establishes a current I = V/R amperes through the resistor.

Now cut the resistance in half. the current now is I = V/(R/2) or 2V/R, twice what it was before.

Do this again: Now you've cut the resistance by a factor of four, and in response the current goes up by a factor of four.

So in the limit of resistance R going to ~(very small), the current I goes to ~(very large). In theory, making R zero drives the current to infinity, but in the real world there are no power supplies that can source infinite current. A real-world power supply facing a very low load resistance will fail to maintain constant voltage and will instead sag down as the load resistance goes to zero.

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A current does not necessarily have to have an electric field to drive it. F.e. in a vacuum electrons can move according Newton's law without the need of an electric field. Only for the start of the move a force is needed. Or a gravitational field may be the driving force. In a closed loop superconductor (shortcut), electrons are circling endlessly. For symmetrical reason, if there was any electric field between 2 points in a homogenous superconductor loop, the electrons would travel in direction of the positive field gradient and also in the opposite direction = negative field gradient, thus compensating any energy transfer. But a perfect conductor is anyway free of a static electric field. Once the electrons are accelerated in a superconductor via a magnetic field, no field is needed to run the electrons in infinite number of circles.

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