Question

A drift velocity of free electrons in a conductor is $v_{d}$, when the current $i$ is flowing in it. If both the radius and current are doubled, the drift velocity will be :

• A. $\frac{v_{d}}{8}$
• B. $\frac{v_{d}}{4}$
• C. $\frac{v_{d}}{2}$
• D. $v_{d}$

Answer 1

Answer: (C)

If the area of cross-section of wire is $A$ and the number of free electrons per unit volume is $n$, then in $t$ seconds $n A v_{d} t$ electrons will pass it.

The electric current is given by
$ i =n e A v_{d} $
$\Rightarrow v_{d} =\frac{i}{n e A}$
where $v_{d}$ is the drift velocity of the electrons.
Given, $r_{1}=r, $
$L_{1}=i, $
$r_{2}=2 r, $
$i_{2}=2 i$
$\frac{v_{d_{1}}}{v_{d_{2}}} =\frac{i_{1}}{i_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}} $
$=\frac{i}{2 i} \times \frac{(2 r)^{2}}{(r)^{2}}=2$
$\Rightarrow v_{d_{2}} =\frac{v_{d_{1}}}{2}$
Note : Direction of drift velocity is opposite to direction of electric field.