Question

Equal potentials are applied on an iron and a copper wire of same length. In order to have the same current flow in the two wires, the ratio r (iron) /r (copper) of their radii must be: [Give that: specific resistance of iron $=1.0\times {10}^{-7}$ ohm-m and specific resistance of copper $=1.7\times {10}^{-8}$ ohm-m]

• A. about 1.2
• B. about 2.4
• C. about 3.6
• D. about 4.8

Answer 1

The correct option is B about 2.4

To have same current flow, Resistance should be same.

and we know that $R=\frac{\rho l}{\pi r^2}$

Keeping same resistance $r^2\propto \rho ⟹r\propto \sqrt{\rho }$

According to question:

$\frac{r_{iron}}{r_{Copper}}=\sqrt{\frac{{\rho }_{iron}}{{\rho }_{copper}}}=\sqrt{\frac{1\times {10}^{-7}}{1.7\times {10}^{-8}}}\approx 2.4$