Question

When current $i$ is flowing through a conductor, the drift velocity is $v$. If the value of current through the conductor and its area of cross-section is doubled, then new drift velocity will be

• A. $4v$
• B. $\frac{v}{2}$
• C. $\frac{v}{4}$
• D. $v$

Answer 1

The correct option is D $v$

$\text{Step 1: Drift velocity in initial case}$

Relation between Current $i$ and Drift velocity $v$ is given by:

$i=neAv$

$\Rightarrow V=\frac{i}{neA}$ $....\left(1\right)$

$\text{Step 2: Drift velocity in final case}$

FInally when current and area $A$ are doubled.

$\therefore i^{\prime }=2i$ and $A^{\prime }=2A$

So, New drift velocity $v^{\prime }$

$\Rightarrow v^{\prime }=\frac{2i}{ne.2A}=\frac{i}{neA}$ $....\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$

$v^{\prime }=v$

Therefore there is no change in drift velocity.

Hence Option $\left(D\right)$ correct.