When 126 V is applied across a wire of 10 m length and 0.30 mm radius, the current density is \( 1.4\times10^{4}\,\mathrm{A/m^2} \). What is the resistivity of the wire?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 9\times10^{-4}\,\Omega\,\mathrm{m} \)
In terms of field and current density, Ohm's law reads \( E = \rho J \). The field in the wire is the potential difference per unit length.
\( \displaystyle E = \frac{V}{L} = \frac{126\,\mathrm{V}}{10\,\mathrm{m}} = 12.6\,\mathrm{V\,m^{-1}} \)
\( \displaystyle \rho = \frac{E}{J} = \frac{12.6}{1.4\times10^{4}} = 9\times10^{-4}\,\Omega\,\mathrm{m} \)