The maximum current that flows through a fuse | vedclass

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Question

(A) The heat generated in a fuse wire of length $l$,radius $r$,and resistivity $\rho$ due to current $I$ is given by $H = I^2 R t = I^2 (\rho l / \pi

Vedclass · Accepted Answer

$r^{3/2}$

Vedclass · Answer

(A) The heat generated in a fuse wire of length $l$,radius $r$,and resistivity $\rho$ due to current $I$ is given by $H = I^2 R t = I^2 (\rho l / \pi r^2) t$.This heat is dissipated through the surface area of the wire via radiation,which is proportional to the surface area $A = 2\pi rl$ and the temperature difference $\Delta T$,following Stefan's Law: $H_{dissipated} \propto (2\pi rl) \Delta T$.At the point of blowing out,the heat generated equals the heat dissipated: $I^2 (\rho l / \pi r^2) \propto 2\pi rl$.Rearranging for $I^2$,we get $I^2 \propto r^3$,which implies $I \propto r^{3/2}$.Therefore,the maximum current is proportional to $r^{3/2}$.

The maximum current that flows through a fuse wire before it blows out varies with its radius as

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