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
A) 3 A
B) $3 \times \sqrt{\frac{3}{2}}$ A
C) $3 \times \left( \ \frac{3}{2} \right)^{3/2}\ $A
D) $3\ \times \left( \frac{3}{2} \right)$ A
Explanation
(c) For a fuse $I^{2} \propto r^{3}$
$\therefore\ \frac{I_{1}^{2}}{I_{2}^{2}} = \frac{r_{1}^{3}}{r_{2}^{2}}$
$\ \frac{3^{2}}{I_{2}^{2}} = \left( \ \frac{0.02}{0.03} \right)^{3}$
$I_{2} = 3 \times \left( \ \frac{3}{2} \right)^{3/2}$A
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.