At \( 20^\circ\mathrm{C} \) the resistance of a copper wire of length 30 m and diameter 0.1 cm is \( 0.65\,\Omega \). The resistivity of copper wire at \( 20^\circ\mathrm{C} \) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 1.702 \times 10^{-8}\,\Omega\,\mathrm{m} \)
The resistance of a wire is \( R = \rho L/A \), so the resistivity is
\( \displaystyle \rho = \frac{R A}{L} = \frac{R\,\pi d^{2}}{4L} \)
\( d = 0.1\,\mathrm{cm} = 1\times10^{-3}\,\mathrm{m} \)
\( L = 30\,\mathrm{m} \)
\( R = 0.65\,\Omega \)
\( \displaystyle A = \frac{\pi d^{2}}{4} = \frac{3.142 \times 10^{-6}}{4} = 7.854\times10^{-7}\,\mathrm{m^{2}} \)
\( \displaystyle \rho = \frac{0.65 \times 7.854\times10^{-7}}{30} = 1.702\times10^{-8}\,\Omega\,\mathrm{m} \)