Question

A current flows in a wire of circular cross section with the free electrons travelling with drift velocity $\overline{V}$. If an equal current flows in a wire of same material and twice the radius, the new drift velocity is:

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

Answer 1

Answer: (A)

Current in the wire $I=Ane\overrightarrow{v_d}$

where $A$ is the cross-section area of the wire and $n$ is the number density of electrons.

$\therefore$ $\overrightarrow{v_d}\propto \frac{1}{A}$

where $A=\pi r^2$

$⟹$ $\overrightarrow{v_d}\propto \frac{1}{r^2}$

Thus we get $\frac{\overrightarrow{v_d}}{\overrightarrow{V}}=\frac{r_1^2}{r_2^2}$

OR $\frac{\overrightarrow{v_d}}{\overrightarrow{V}}=\frac{r^2}{(2r{)}^2}=\frac{1}{4}$

$⟹$ $\overrightarrow{v_d}=\frac{\overrightarrow{V}}{4}$