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For this question, I'm assuming the current is continuous, the shape of the wire is cylindrical, and the air is STP air.

(I bridged a fuse with a piece of soldering wire, and I'd like to be stupid in the most scientific way possible.)

Emmanuel Lopez
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    Just because you tagged your question with #math, #theory and #overheat. In addition to the answer that recommends you fit a proper fuse (and it is what you need if you are really concerned with a fuse capability of your piece of wire). To compute a current which melts down the wire, is a problem of electrothermal analysis. To solve this electrothermal analysis problem, you need more data than just dimensions and resistivity of the wire, as melting temperature of the material, latent heat of melting, electric resistivity and thermal resistance as functions of temperature, etc. – V.V.T Oct 09 '22 at 10:52

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There's more to a fuse than burning a wire so that it becomes an open circuit: -

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Image from this question and answer. In the title of the question are the words "what does the spring do" and here's the scientific part that maybe you didn't know about.

When the fuse wire melts, if the spring doesn't recoil (and open the gap where the wire melted), there can be enough open-circuit voltage to produce an arc that continues to carry current and, of course this is dangerous.

I bridged a fuse with a piece of soldering wire, and I'd like to be stupid in the most scientific way possible

Hopefully, you can probably see why it's not just down to burning a piece of solder. Fit a proper fuse; if a fire occurred due to not using a proper fuse how would you feel and how might your home insurance people feel.

Andy aka
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