Question

In a wire of cross-section 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 $2v$?

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

Answer 1

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

For the given wires of same material current flowing through them is
$I_1=ne{A}_{1}v$ ....................................(1)
$I_2=ne{A}_2\left(2v\right)$ .............................................(2)
where, all variables have their usual meanings.
As per the given data, $A_1=\pi r^2$ and $A_2=\pi (\frac{r}{2}{)}^2$
using these values in equation (1) and (2)
$I_1=ne\pi r^{2}v$ ...................(3)
and
$I_2=ne\pi \left(\frac{r}{2}{)}^2\right(2v)$
$I_2=ne\pi \left(\frac{r^2}{4}\right)\left(2v\right)$
$I_2=\frac{\left(ne\pi r^{2}v\right)}{2}$
$\therefore I_2=\frac{I_1}{2}$ ..............from(3)