Question

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

• A. v/4
• B. v/2
• C. 2v
• D. 4v

Answer 1

The correct option is D 4v

Let I be the current flow through wire.

Let V be the drift velocity of wire which has diameter d.

Let A be the area of wire.

Consider a wire of same material but diameter is half

Therefore, Area =$\frac{A}{4}$

Since, $I=NeAV$

N is same for both wire because both of them made of same material.

$I_1=I_2$

$Ne{A}_1{V}_1=Ne{A}_2{V}_2$

$AV=\frac{A}{4}{V}_2$

$V_2=4V$