What is the conductivity of a wire of resistance \( 0.05\,\Omega \), area of cross section \( 2\times10^{-4}\,\mathrm{m^{2}} \) and length 50 cm?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 5\times10^{4}\,\Omega^{-1}\mathrm{m^{-1}} \)
The resistance of a wire is \( R = \rho\frac{l}{A} \), and the conductivity is the reciprocal of the resistivity, \( \sigma = \frac{1}{\rho} \). Hence \( \sigma = \frac{l}{RA} \).
Length in metres: \( l = 50\,\mathrm{cm} = 0.5\,\mathrm{m} \).
\( \displaystyle \sigma = \frac{l}{RA} = \frac{0.5\,\mathrm{m}}{0.05\,\Omega\times2\times10^{-4}\,\mathrm{m^{2}}} \)
\( \displaystyle \sigma = \frac{0.5}{10^{-5}}\,\Omega^{-1}\mathrm{m^{-1}} = 5\times10^{4}\,\Omega^{-1}\mathrm{m^{-1}} \)