Question

The drift velocity of the free electrons in a conducting wire carrying a current ${}^{\prime }{i}^{\prime }$ is $v$. If in a wire of the same metal, but of double the radius and the current to be $2i,$ then the drift velocity of the electrons will be ?

Answer 1

We know that ,

$i=neA{v}_d$

$v_d=\frac{i}{neA}$

$\because A=\pi r^2$

$v_d\propto \frac{i}{r^2}$

So, $v\propto \frac{i}{r^2}.......\left(1\right)$

When current and radius are doubled,

$v^{{}^{\prime }}\propto \frac{2i}{4r^2}.......\left(2\right)$

Dividing $\left(2\right)$ by $\left(1\right)$ we get,

$\frac{v^{{}^{\prime }}}{v}=\frac{1}{2}$

$v^{{}^{\prime }}=\frac{v}{2}$