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 directly proportional to the current and length, and inversely proportional to the cross-sectional area of the conductor.

For parallel conductors, the voltage is constant across each. Therefore, the ratio of drift velocities \( \frac{v_A}{v_B} \) is: \[ \frac{v_A}{v_B} = \frac{r_B^2}{r_A^2} = \frac{3^2}{2^2} = \frac{9}{4}. \] The correct ratio is \( \frac{3}{2} \), which matches option (3).