Question

An electric cell of e.m.f. 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 of electrons in a conductor is given as

$v_d=\frac{m\sigma E}{nedl}$

where $\sigma$ is the conductivity of the conductor

$m$ is the mass of electrons

$n$ is the density of electrons

$d$ is the density of conductor

$l$ is the lenght of conductor

Hence $v_d\propto \frac{1}{l}$

Thus when the length of wire is doubled, the drift velocity halves.