Question

Two wires A and B are made up of the same material and have the same mass. Wire A has radius of \(2.0 \mathrm{~mm}\) and wire B has radius of 4.0 mm. The resistance of wire \(\mathrm{B}\) is \(2 \Omega\). The resistance of wire A is ______  \(\Omega\).

Answer 1

Correct answer is : 32

\(\because \mathrm{R}=\frac{\rho \ell}{\mathrm{A}}=\frac{\rho \mathrm{V}}{\mathrm{A}^{2}}\)

\( \begin{aligned} & \therefore \frac{\mathrm{R}_{\mathrm{A}}}{\mathrm{R}_{\mathrm{B}}}=\frac{\mathrm{A}_{\mathrm{B}}^{2}}{\mathrm{~A}_{\mathrm{A}}^{2}}=\frac{\mathrm{r}_{\mathrm{B}}^{4}}{\mathrm{r}_{\mathrm{A}}^{4}} \\ & \Rightarrow \frac{\mathrm{R}_{\mathrm{A}}}{2}=\left[\frac{4 \times 10^{-3}}{2 \times 10^{-3}}\right]^{4} \\ & \Rightarrow \mathrm{R}_{\mathrm{A}}=32 \ \Omega \end{aligned} \)