Question

A conductor has an area of cross section $S$. If the electron charge is '$e$' and the drift velocity of '$m$' number of free electrons is '$v_D$',then the ratio of $v_D$ to the current $i$ flowing through the conductor is given by:

• A. $Sem$
• B. $(Sem{)}^{-1}$
• C. $Sm{e}^{-1}$
• D. $Se{m}^{-1}$

Answer 1

The correct option is B $(Sem{)}^{-1}$

The current $i$ flowing through a conductor having an area of cross section $A$ is given by:
$i=neA{v}_D$

where, $n$ is the number of free electrons present (per $m^3$), $v_D$ is the drift velocity and $e$ is the electron charge.

Given: $n=m$, $A=S$
$⟹i=meS{v}_D$
$⟹\frac{i}{v_D}=meS=Sem$
Hence, $\frac{v_D}{i}=(Sem{)}^{-1}$