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

Options

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

Answer

D

Explanation

Drift velocity `v_(d)=(l)/(nAe)=(lxx4)/(n pi D^(2)e) " " [because A = pi((D)/(2))^(2)]`
i.e., `v_(d) prop (1)/(D^(2)) therefore (v_(d_(1)))/(v_(d_(2)))=(D_(2)^(2))/(D_(1)^(2))=((1)/(2))^(2)=(1)/(4)`