Question

The drift velocity of free electrons is $v$ on passing current $i$ in a conducting wire. Drift velocity of electrons in the same wire having twice the radius and current $2i$ will be:

• A. $v$
• B. $4v$
• C. $\dfrac{v}{2}$
• D. $\dfrac{v}{4}$

Hint:

Drift velocity is inversely proportional to the cross-sectional area of the wire.

Answer 1

The Correct Option is C

Step 1: Formula for drift velocity.
\[ v_d = \frac{I}{n e A} \] where $A = \pi r^2$.
Step 2: Compare two cases.
Initial case: \[ v = \frac{i}{n e \pi r^2}. \] New case (radius $= 2r$, current $= 2i$): \[ v' = \frac{2i}{n e \pi (2r)^2} = \frac{2i}{4 \, n e \pi r^2} = \frac{1}{2} \cdot \frac{i}{n e \pi r^2}. \]
Step 3: Conclusion.
\[ v' = \frac{v}{2}. \] Hence the correct answer is (C) $\dfrac{v}{2}$.