Question

A fuse wire with a radius of 1 mm blows at 1.5 A. If the fuse wire of the same material should below at 3.0 A, the radius of the wire must be

• A. 4${}^{1/3}$ mm
• B. $\sqrt{2}$mm
• C. $0.5mm$
• D. $8.0mm$

Answer 1

Answer: (A)

4${}^{1/3}$ mm

The temperature of the wire increase to such a value at which, the heat
produced per second equal heat lost per second due to radiation i.e. $I^{2}R=H\times \left(2\pi rl\right)$ where H is heat lost per second per unit area due to radiation.

or $I^2\left(\frac{\rho l}{\pi r^2}\right)=H\times \left(2\pi rl\right)$

so, $I^2\propto r^3$

here, $\frac{I_1^2}{I_2^2}=\frac{r_1^3}{r_2^3}$

or $r_2={\left(\frac{I_2}{I_1}\right)}^{2/3}\times r_1={\left(\frac{3}{1.5}\right)}^{2/3}\times 1=2^{2/3}=4^{1/3}$ mm