Question

Two wires of the same material but of different diameters carry the same current I. If the ratio of their diameters is 1 : 2, then the corresponding ratio of their mean drift velocities will be

• A. 4 : 1
• B. 1 : 1
• C. 1 : 2
• D. 1 : 4

Answer 1

The correct option is A 4 : 1

from wire 1, $A_1=\frac{\pi D^2}{4}$
from wire 2, $A_2=\pi D^2$
the mean drift velocity $\propto \frac{1}{Area}$
$V_{drift}\propto \frac{1}{Area}$
$\frac{V_1}{V_2}=\frac{A_2}{A_1}=\frac{\pi D^2}{\frac{\pi D^2}{4}}$

$\frac{V_1}{V_2}=\frac{4}{1}$