Question

Two conductors A and B of the same material have their lengths in the ratio 1:2 and radii in the ratio 2:3. If they are connected in parallel across a battery, the ratio \( \frac{v_A}{v_B} \) of the drift velocities of electrons in them will be:

• A. 2
• B. \( \frac{1}{2} \)
• C. \( \frac{3}{2} \)
• D. \( \frac{8}{9} \)

Hint:

Drift velocity is related to the current and the area of cross-section. Smaller area of cross-section leads to larger drift velocity.

Answer 1

The Correct Option is C

The drift velocity \( v \) is inversely proportional to the area of cross-section of the conductor, and directly proportional to the current and length. Since the conductors are in parallel, the voltage is the same across both. Hence, the ratio of drift velocities \( \frac{v_A}{v_B} \) is: \[ \frac{v_A}{v_B} = \frac{r_B^2}{r_A^2} = \frac{3^2}{2^2} = \frac{9}{4}. \] Thus, the correct ratio is \( \frac{3}{2} \), corresponding to option (3).