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Factors Affecting Melting Point

The maximum c...

Question

The maximum current $I$ , which can be passed through a fuse without melting varies with its radius $r$ as:

I \propto r

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I \propto r^{3 / 2}

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I \propto r^{2}

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I \propto (1 / r^{2})

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Solution

The correct option is B $I \propto r^{3 / 2}$
Heat lost per second per unit surface area of fuse wire is
$H = \frac{I^{2} ρ}{2 π^{2} r^{3}}$
$\Rightarrow I^{2} \propto r^{3}$
$\Rightarrow I \propto r^{\frac{3}{2}}$

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