What is immaterial for an electric fuse wire?

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(C) The heating effect in a fuse wire is governed by Joule's law of heating,given by $H = I^2Rt$. The resistance $R$ of a wire is given by $R = \rho \

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Its length

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(C) The heating effect in a fuse wire is governed by Joule's law of heating,given by $H = I^2Rt$. The resistance $R$ of a wire is given by $R = \rho \frac{L}{A} = \rho \frac{L}{\pi r^2}$. Substituting this into the heat equation,we get $H = I^2 (\rho \frac{L}{\pi r^2}) t$. The fuse melts when the heat generated reaches a critical value. Since the heat generated $H$ is proportional to the length $L$,one might think it matters; however,for a given fuse wire material and radius,the current required to melt the fuse is independent of its length because the heat dissipation per unit length remains constant. Thus,the length is immaterial for the functioning of an electric fuse wire.

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