What is immaterial for an electric fuse wire?

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Question

(C) The heating effect in a fuse wire is governed by Joule's law of heating,given by $H = I^2 R t$,where $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2

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Length of the wire

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(C) The heating effect in a fuse wire is governed by Joule's law of heating,given by $H = I^2 R t$,where $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$.For a fuse to melt at a specific current $I$,the heat generated must be sufficient to raise the temperature to the melting point.Since the heat generated depends on the resistance $R$,which is proportional to the resistivity $\rho$ and inversely proportional to the square of the radius $r$,these factors are critical.The current $I$ is the threshold value the fuse is designed for.The length $l$ of the wire does not affect the current-carrying capacity or the melting point of the fuse wire,as the heat generated per unit length is what matters for the fuse's operation. Thus,the length is immaterial.

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