Question

An electric cell of emf $E$ is connected across a copper wire of diameter $d$ and length $l$. The drift velocity of electrons in the wire is $v_d$. If the length of the wire is changed to $2l$, the new drift velocity of electrons in the copper wire will be:

• A. $v_d$
• B. $2v_d$
• C. $v_d/2$
• D. $v_d/4$

Answer 1

Answer: (C)

$v_d/2$

The drift velocity is given as
$v_d=\frac{i}{neA}=\frac{E}{R\times neA}$
$=\frac{E\times A}{\rho l\times neA}=\frac{E}{\rho lne}$
When length of wire changed to $2l$, the new drift velocity
${v^{\prime }}_d=\frac{E}{\rho \times 2l\times ne}$
$\therefore \frac{{v^{\prime }}_d}{v_d}=\frac{\frac{E}{\rho 2lne}}{\frac{E}{\rho lne}}=\frac{1}{2}$
$\Rightarrow {v^{\prime }}_d=\frac{v_d}{2}$