Two conductors A and B are made of same material and have same length. A is a solid wire of diameter 2 mm and B is a hollow tube of outer diameter 4 mm and inner diameter 2 mm. The ratio of resistances RA and RB of two conductors, respectively, will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3 : 1
For conductors of the same material and length, resistance is inversely proportional to the area of cross-section.
\( \displaystyle R = \frac{\rho l}{A} \;\Rightarrow\; R \propto \frac{1}{A} \)
The solid wire has radius 1 mm. The tube has outer radius 2 mm and inner radius 1 mm, so its area is the area of a ring.
\( A_A = \pi (1\,\mathrm{mm})^{2} = \pi\,\mathrm{mm^{2}} \)
\( \displaystyle A_B = \pi\left[(2\,\mathrm{mm})^{2} - (1\,\mathrm{mm})^{2}\right] \)
\( A_B = 3\pi\,\mathrm{mm^{2}} \)
\( \displaystyle \frac{R_A}{R_B} = \frac{A_B}{A_A} = \frac{3\pi}{\pi} \)
\( R_A : R_B = 3 : 1 \)
Note: NTA picked this question from an NCERT Exemplar problem and changed the figures. Do not ignore the Exemplar while practising numericals.
NCERT Exemplar:
Current Electricity – …
