Question

A fuse wire with a circular cross-section and having diameter of 0.4 mm blows with a current of 3 A. The value of 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

• A. 3 A
• B. $3\times \sqrt{\frac{3}{2}}A$
• C. $3\times {\left(\frac{3}{2}\right)}^{3/2}A$
• D. $3\times \frac{3}{2}A$

Answer 1

Answer: (C)

Relation for fuse wire is
$i^2\propto r^3$
${\left(\frac{i_1}{i_2}\right)}^2={\left(\frac{r_1}{r_2}\right)}^3$
${\left(\frac{3}{i_2}\right)}^2={\left(\frac{0.4}{0.6}\right)}^3$
${\left(\frac{3}{i_2}\right)}^2={\left(\frac{2}{3}\right)}^{3/2}$
$i_2=3\times {\left(\frac{3}{2}\right)}^{3/2}A$