A 10 m long wire of diameter 0.4 mm has a resistance of 2.0 Ω. The resistivity of the material of the wire is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 2.5 × 10−8 Ωm
Resistance depends on the dimensions of the wire through \( R = \rho L/A \), where A is the area of cross-section, found from the radius (half the diameter).
\( \displaystyle A = \frac{\pi d^{2}}{4} = \frac{\pi \times (0.4\times10^{-3}\,\mathrm{m})^{2}}{4} \)
\( \displaystyle A \approx 1.257\times10^{-7}\,\mathrm{m^{2}} \)
\( \displaystyle \rho = \frac{RA}{L} \)
\( \displaystyle \rho = \frac{2.0\,\Omega \times 1.257\times10^{-7}\,\mathrm{m^{2}}}{10\,\mathrm{m}} \)
\( \displaystyle \rho \approx 2.5\times10^{-8}\,\Omega\,\mathrm{m} \)