A fuse wire with a circular cross-section and having diameter of 0.4 mm blows with a current of 3 amp. The value of the current for which another fuse wire made of the same material but having circular cross-section with diameter of 0.6 mm will blow is

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$3 \times (3 / 2) amp$

$3 \times \sqrt{(3 / 2)} amp$

3 amp

$3 \times (3 / 2)^{3 / 2} amp$

answer is D.

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Detailed Solution

For a fuse wire $i^{2} \propto r^{3}$
$∴ \frac{{i_{1}}^{2}}{{i_{2}}^{2}} = \frac{{r_{1}}^{3}}{{r_{2}}^{3}} where r_{1} = \frac{0 \cdot 04}{2} = 0 \cdot 02 cm$
and $I_{2} = \frac{0 \cdot 06}{2} = 0 \cdot 03 cm$
$∴ \frac{(3)^{2}}{i_{2}^{2}} = {(\frac{0 \cdot 02}{0 \cdot 03})}^{3} = {(\frac{2}{3})}^{3}$
or $i_{2}^{2} = (3)^{2} {(\frac{3}{2})}^{3}$
or $i_{2} = 3 \times {(\frac{3}{2})}^{3 / 2}$

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