A uniform wire of diameter $d$ carries a current of 100 mA when the mean drift velocity of electrons in the…
A uniform wire of diameter $d$ carries a current of 100 mA when the mean drift velocity of electrons in the wire is $v$. For a wire of diameter $\frac{d}{2}$ of the same material to carry a current of 200 mA , the mean drift velocity of electrons in the wire is
$4 v$
$8 v$
$v$
$2 v$
Solution
current $i=n A v_d \mathrm{e}$
( $v_d=$ mean drift velocity $)$
$=n\left(\frac{\pi D^2}{4}\right) v_d e$
$\therefore i \propto D^2 v_d$
$\frac{100}{200}=\frac{(d)^2}{\left(\frac{d}{2}\right)^2} \times \frac{v}{v^{\prime}}$
$\Rightarrow v^{\prime}=2 \times 2^2 v=8 v$
.