Question

A current $I$ flows through a uniform wire of diameter $d$ when the mean electron drift velocity is $v$. The same current will flow through a wire of diameter $\frac{d}{2}$ made of the same material if the mean drift velocity of the electron is

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

Answer 1

The correct option is D $4v$

The current $I$ in the uniform wire of diameter $d_1$ i.e.

radius $r_1$ with mean electron drift velocity $v_1$ is given by,

$I=ne4\pi (r_1{)}^2{v}_1$

if the same current flows through the wire of diameter $\frac{d_1}{2}$ i.e radius $\frac{r_1}{2}$ with drift velocity $v_2$ is given by

$I=ne4\pi {\left(\frac{r_1}{2}\right)}^2{v}_2$
Therefore we can write

$I=ne4\pi (r_1{)}^2{v}_1=ne4\pi {\left(\frac{r_1}{2}\right)}^2{v}_2$

$\Rightarrow v_1=\frac{v_2}{4}$

$\therefore v_2=4v_1$