Question

A current I flows through a uniform wire of diameter d when the electron drift velocity is V .The same current will flow through a wire of diameter d/2 made of the same material if the drift velocity of the electrons is

• A. v/4
• B. v/2
• C. 2v
• D. 4 v

Answer 1

The correct option is A v/4

The relation between current and drift velocity is

$I=neA{v}_d$

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

$v_d=\frac{I}{ne\pi r^2}$

According to given data,

$v_d^{{}^{\prime }}=\frac{1}{ne\pi {\left(2r\right)}^2}$

$v_d^{{}^{\prime }}=\frac{1}{4}\frac{1}{ne\pi r^2}$

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