The resistance of a cylindrical conductor is:

The correct answer is Option (3) → inversely proportional to the square of the radius

The resistance of a conductor of resistivity \( \rho \), length \( l \) and cross-sectional area \( A \) is

    \( \displaystyle R = \frac{\rho\,l}{A} = \frac{\rho\,l}{\pi r^{2}} \)

So \( R \) is directly proportional to the length and inversely proportional to the square of the radius.

NCERT (2026-27):
Ohm’s Law – “… Thus, doubling the length of a conductor doubles the resistance. In general, then resistance is proportional to length,

    \( \displaystyle R \propto l \qquad (3.5) \)”

Ohm’s Law – “… Thus, halving the area of the cross-section of a conductor doubles the resistance. In general, then the resistance R is inversely proportional to the cross-sectional area,

    \( \displaystyle R \propto \frac{1}{A} \qquad (3.7) \)”