There are two conductor X and Y of the same material, having length l and 4l, and radii r and \( \displaystyle\frac{r}{4} \) respectively. The ratio of their resistance is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1 : 64
The resistance of a conductor is \( R = \rho\,\displaystyle\frac{l}{A} \) with \( A = \pi r^{2} \). The material is the same, so the resistivity \( \rho \) is the same for X and Y and cancels in the ratio.
\( R_X = \rho\,\displaystyle\frac{l}{\pi r^{2}},\qquad R_Y = \rho\,\displaystyle\frac{4l}{\pi (r/4)^{2}} = 64\,\rho\,\displaystyle\frac{l}{\pi r^{2}} \)
\( \displaystyle \frac{R_X}{R_Y} = \frac{1}{4\times16} = \frac{1}{64} \)