Question

A current $\left(I\right)$ flows through a uniform wire of diameter $\left(d\right),$ when the mean drift velocity is $V$. If same current flows through a wire of diameter $d/2$ made of the same material, then the mean drift velocity of the electron is

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

Answer 1

The correct option is C $4V$

Given: Drift velocity $V_{d_1}=V$

$V_{d_2}=?$

We know that the current flow through the conductor is given by,

$I=neA{v}_d$

$\Rightarrow V_d\propto \frac{1}{A}\propto \frac{1}{\frac{\pi d^2}{4}}\propto \frac{1}{d^2}$

$\frac{V_{d_1}}{V_{d_2}}=\frac{(d/2{)}^2}{d^2}=\frac{1}{4}$

$V_{d_2}=4V$