The resistivity of an iron wire is \( 10\times10^{-8}\,\Omega\,\mathrm{m} \). The resistance of an iron wire is \( 5\,\Omega \). If its length as well as thickness is doubled then its resistivity will be:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 10\times10^{-8}\,\Omega\,\mathrm{m} \)
Resistivity is a property of the material (and its temperature), not of the size or shape of the wire. Changing the length and thickness changes the resistance \( R = \rho l/A \), but not \( \rho \).
\( \rho = 10\times10^{-8}\,\Omega\,\mathrm{m} \) (unchanged)
NCERT (2026-27):
Ohm’s Law – “… Combining Eqs. (3.5) and (3.7), we have
\( \displaystyle R \propto \frac{l}{A} \qquad (3.8) \)
and hence for a given conductor
\( \displaystyle R = \rho\,\frac{l}{A} \qquad (3.9) \)
where the constant of proportionality ρ depends on the material of the conductor but not on its dimensions. ρ is called resistivity.”