Question

In the wire of cross-sectional radius $r$, free electrons travel with drift velocity $v$ when a current $I$ flows through the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is $2v$?
$[$Assume same electron density$]$

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

Answer 1

The correct option is C $\frac{I}{2}$

We know that,
$i=neA{v}_d$

For same electron density,
$i\propto A{v}_d$ or $r^2{v}_d$ $[\because A=\pi r^2]$

$\therefore \frac{i_1}{i_2}=\frac{r_1^2{v}_{d1}}{r_2^2{v}_{d2}}$

$\Rightarrow \frac{I}{i_2}=\frac{r^2\times v}{(r/2{)}^2\times 2v}=2$

$\Rightarrow i_2=\frac{I}{2}$