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 × 10^–7Ωm and that of

copper = 1.7 × 10^–8Ωm]

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

Answer 1

Answer: (B)

About 2.4

Answer 2

V = constant., i = constant. So R = constant

⇒ $\frac{P_{i}l_{i}}{A_{i}} = \frac{\rho_{Cu}l_{Cu}}{A_{Cu}} \Rightarrow \frac{\rho_{i}l_{i}}{r_{i}^{2}} = \frac{\rho_{Cu}l_{Cu}}{r_{Cu}^{2}}$

⇒ $\frac{r_{i}}{r_{Cu}} = \sqrt{\frac{\rho_{i}}{\rho_{Cu}}} = \sqrt{\frac{1.0 \times 10^{- 7}}{1.7 \times 10^{- 8}}} = \sqrt{\frac{100}{17}} \approx 2.4$