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 $