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Pardon me if this is too basic knowledge. It's been a while since my last Physics class in high school so a lot of the knowledge is no longer active in my mind. Here's the question.

Say I have a battery of 2V and use a short wire made of superconducting material (R->0) to connect the two terminals. If P=V^2/R, does that mean I just create superpower?

In another scenario, I have a wire loop connecting to a resistor (R) made of superconducting material. Let's say I use my power (P_input) to generate a consistent change in the magnetic field across the loop, which in turn creates an electromotive force of 2V inside the loop. Neglecting the resistance of the wire, if P_output=V^2/R and R -> 0, then P_output must be extremely high, while P_input stays the same, which doesn't really make sense. Where is the mistake in this reasoning?

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Your mistake is assuming that the battery is capable of that level of power output. In reality either the battery or the wire burn up.

Simplified equations such as ohm's law don't really capture the notion of power output limits. In the AC world power limits are established by measuring drops in voltage or frequency. So my point is that there is a limit on power output, even if the equations suggest it goes "to infinity".

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  • $\begingroup$ Could you give me some pointers for more precise equations? $\endgroup$
    – ideals_go
    Dec 26, 2021 at 17:51
  • $\begingroup$ en.wikipedia.org/wiki/Power-flow_study - This is for AC circuits but the principle is consistent. Power flow limits are fundamental to operating a power system. $\endgroup$
    – michael b
    Dec 26, 2021 at 19:29
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No, you won't "create super power" you will just be shorting out the battery. Regarding the formula, perhaps you've forgotten that any cell has internal resistance, so the power output would not be infinite. Technically it wouldn't be "output" because it would stay in the battery, which would be damaged in the short term and destroyed in the longer term, but how long it would take would depend very much on the type of battery. The battery would get hot, and I believe, if it was a lithium battery it could cause a fire.

Regarding the second question, electromagnetic force is measured in Newtons, not Volts. You mentioned a "superconducting resistor". That sounds a bit like "chocolate teapot" but more exactly it is a contradiction in terms because a superconductor has no resistance at all. So, again, if the power source was a battery, it would essentially be the first example again.

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  • $\begingroup$ My bad, it should have been 'electromotive force'. Edited. Would it still the the first example? $\endgroup$
    – ideals_go
    Dec 26, 2021 at 18:25

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