Question

A current '$I$' flows through a metallic wire of radius '$r$' and the free electrons in it drift with a velocity $v_d$. Calculate the drift velocity of the free electrons through the wire of the same material, having double the radius, when some current flows through it.

Answer 1

$I=neA{v}_d$

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

New drift velocity$=v_d^{\prime }=\frac{I}{ne(2r{)}^2}$

$\frac{v_d}{v_d^{\prime }}=\frac{\frac{I}{ne(2r{)}^2\times 2}}{\frac{I}{ne2\times r^2}}$

$\frac{v_d}{v_d^{\prime }}=\frac{r^2}{4r^2}$

$v_d^{\prime }=\frac{v_d}{4}=\frac{1}{4}th$ of the original