Question

Equal potentials are applied on an iron and copper wire of same length. In order to have same current flow in the wire, the ratio $\left(\frac{r_{iron}}{r_{copper}}\right)$ of their radii must be [ Given that specific resistance of iron $=1.0\times {10}^{-7}\Omega m$ and that of copper $=1.7\times {10}^{-8}\Omega m$ ]

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

Answer 1

Answer: (B)

About 2.4

V = constant, i = constant. So R = constant
$\Rightarrow \frac{{\rho }_i{l}_i}{A_i}=\frac{{\rho }_{Cu}{l}_{Cu}}{A_{Cu}}\Rightarrow \frac{{\rho }_i{l}_i}{r_i^2}=\frac{{\rho }_{Cu}{l}_{Cu}}{r_{Cu}^2}\Rightarrow \frac{r_i}{r_{Cu}}=\sqrt{\frac{{\rho }_i}{{\rho }_{Cu}}}=\sqrt{\frac{1.0\times {10}^{-7}}{1.7\times {10}^{-8}}}=\sqrt{\frac{100}{17}}\approx 2.4$