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What would happen if I were to connect two ends of a battery with a magic wire of no resistance?

In the conceptual scheme of modeling circuit behavior there is always a circuit with a resistor given and the voltage drop across the resistor element is equal to the voltage supplied by the emf source.This resistor is often depicted as a lumped matter abstraction in our circuit diagrams, connected by wires which have 0 resistance. I was wondering what would happen if we were to connect the ends of a battery with one such wire with no element in between. Although this is impossible in real life, keeping in mind the abstractions of our model, could someone explain what would happen and how this phenomenon be explained in lieu of our abstract model?

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    $\begingroup$ physics.stackexchange.com/q/8675 and physics.stackexchange.com/q/188393 $\endgroup$
    – BowlOfRed
    Nov 3, 2016 at 8:07
  • $\begingroup$ Some answers in these posts take into consideration the internal resistance of the battery. I am not asking this. Consider an ideal voltage source and an ideal wire connected to it. How can one explain what happens in this case? $\endgroup$
    – SaitamaSensei
    Nov 3, 2016 at 8:20
  • $\begingroup$ Chemical action in a battery is rate-limited, just as if a resistance was present (and may be called 'internal resistance' when communicating with non-chemists). The nature of the chemical reaction determines a rate at which chemical reactions in a shorted battery produce energy, which will at least partly be heat. $\endgroup$
    – Whit3rd
    Nov 4, 2016 at 6:35

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Electrical circuit diagrams are graphical representations of the reality, that is, they are graphical models. These graphical models are composed of fancy symbols representing devices and lines representing interconnections.

To this graphical representation corresponds a mathematical representation, a mathematical model, composed of mathematical symbols and relationships among them. To each graphical symbol corresponds a specific relationship between certain quantities associated to the symbol (a constitutive equation), and to the interconnections between the graphical symbols correspond relationships between quantities associated to different graphical symbols.

What happens in this abstract model when you short-circuit the two poles of a battery? It happens that you obtain a set of equations which has no solutions, assuming that the relationships are defined over the reals. If you consider the extended real line, which contains the symbol of infinity, you would obtain that the current through the circuit is infinite.

What would happen in real life? Don't try it at home.

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  • $\begingroup$ Does this mean ohms law breaks down in this case and we can't mathematically model this scenario? $\endgroup$
    – SaitamaSensei
    Nov 3, 2016 at 8:19
  • $\begingroup$ @SaitamaSensei I'm pretty sure that battery manufacturers must model this scenario (short circuit). One simple way to model this is that batteries have internal impedance, in a short-circuit situation, this internal impedance leads to heating and that leads to chemical and physical breakdown of the battery. $\endgroup$
    – RedGrittyBrick
    Nov 3, 2016 at 11:10

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