Question

A fuse wire with radius $1mm$ blows at $1.5A$. The radius of the fuse wire of the same material to blow at $3A$ will be:

• A. $3^{1/4}mm$
• B. $4^{1/3}mm$
• C. $3^{1/2}mm$
• D. $2^{1/3}mm$

Answer 1

Answer: (B)

$4^{1/3}mm$

For fusing current, its relation with radius is given as: $I^2\propto r^3$

$\Rightarrow {\left(\frac{I_2}{I_1}\right)}^2={\left(\frac{r_2}{r_1}\right)}^3$

$\Rightarrow r_2=r_1{\left(\frac{I_2}{I_1}\right)}^{2/3}$

$\Rightarrow r_2=1{\left(\frac{3}{1.5}\right)}^{2/3}$

$\Rightarrow r_2={\left(2\right)}^{2/3}=4^{1/3}mm$