The resistivity of a \( 10\,\mathrm{m} \) long wire of diameter \( 0.4\,\mathrm{mm} \) having a resistance of \( 2\,\Omega \) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 2.5\times10^{-8}\,\Omega\mathrm{m} \)
The resistance of a wire is \( R = \rho l/A \), so the resistivity is \( \rho = RA/l \), with \( A \) found from the radius (half the diameter).
\( d = 0.4\,\mathrm{mm} = 4\times10^{-4}\,\mathrm{m}, \quad r = 2\times10^{-4}\,\mathrm{m} \)
\( A = \pi r^{2} = 3.14\times(2\times10^{-4}\,\mathrm{m})^{2} = 1.256\times10^{-7}\,\mathrm{m^{2}} \)
\( \displaystyle \rho = \frac{RA}{l} = \frac{2\,\Omega\times1.256\times10^{-7}\,\mathrm{m^{2}}}{10\,\mathrm{m}} \)
\( \rho \approx 2.5\times10^{-8}\,\Omega\,\mathrm{m} \)
Note: A similar question was also asked in CUET (UG) 2025 on 14-05-2025 (Slot 2).