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  4. The maximum current that flows in the fuse wire, before it blows out, varies with the radius r as

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Q. The maximum current that flows in the fuse wire, before it blows out, varies with the radius $r$ as

BHUBHU 2008Electromagnetic Induction

Solution:

If $I$ is the safe current through the fuse wire and $h$ is the rate of loss of heat in steady state,
$I^{2} R=h A$
Or $I^{2}\left(\frac{\rho L}{\pi r^{2}}\right)=h \times 2 \pi r L$
Or $I \propto r^{3 / 2}$