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Q.

A fuse wire with a circular cross-sectional radius of 0.02 mm blows with a current of 5 ampere. For what current, another fuse wire made from the same material with cross-sectional radius of 0.04 m wiII blow ?

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a

1 .5 amp

b

3 amp

c

5 amp

d

14. 7 amp

answer is D.

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Detailed Solution

We know that the safe current for a fuse $\propto r^{3 / 2}$
where r is the radius of fuse wire.
$∴ \frac{i_{2}}{i_{1}} = {(\frac{r_{2}}{r_{1}})}^{3 / 2}$
i₁ = 5amp.,r₁ = 0.02mm and r₂ = 0.04mm
$∴ \frac{i_{2}}{5} = {(\frac{0 \cdot 04}{0 \cdot 02})}^{3 / 2} = \sqrt{8}$
or $i_{2} = 5 \sqrt{8} = 10 \sqrt{2} = 14 \cdot 7 amp$

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