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

Question

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 (A) 3 A (B) 3 × √(3/2) A (C) 3 ×((3/2))3/2 A (D) 3 ×((3/2)) A

Tardigrade Admin · Accepted Answer

For a fuse, I2 propto r3 (I12/I22) =(r13/r22) (32/I2) =((0.02/0.03))3 I2 =3 ×((3/2))3 / 2 A

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

3 A

$3 \times \frac{3}{2} A$

$3 \times (\frac{3}{2})^{3/2} A$

$3 \times (\frac{3}{2}) A$

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

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

3 A

3×23​​A

3×(23​)3/2A

3×(23​)A

For a fuse, I2∝r3 I22​I12​​=r22​r13​​ I232​=(0.030.02​)3 I2​=3×(23​)3/2A

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

$3 \times \frac{3}{2} A$

$3 \times (\frac{3}{2})^{3/2} A$

$3 \times (\frac{3}{2}) A$

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