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  4. A fuse wire of circuit cross-section and having diameter of 0.4 mm, allows 3 A of current to pass through it. But if another fuse wire of same material and circular cross-section and having diameter of 0.6 mm is taken, then the amount of current passed through the fuse is

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Q. A fuse wire of circuit cross-section and having diameter of $0.4 \,mm$, allows $3 \,A$ of current to pass through it. But if another fuse wire of same material and circular cross-section and having diameter of $0.6 \,mm$ is taken, then the amount of current passed through the fuse is

Current Electricity

Solution:

For a fuse, $I^{2} \propto r^{3}$
$\frac{I_{1}^{2}}{I_{2}^{2}} =\frac{r_{1}^{3}}{r_{2}^{2}} $
$\frac{3^{2}}{I^{2}} =\left(\frac{0.02}{0.03}\right)^{3} $
$I_{2} =3 \times\left(\frac{3}{2}\right)^{3 / 2} A $