Question

Which of the following options, which describe the dependence of drift velocity $v_d$ on electric field $E,$ obeys Ohm's law?

• A. $v_d\propto E$
• B. $v_d\propto E^2$
• C. $v_d\propto \sqrt{E}$
• D. $v_d$= constant

Answer 1

The correct option is A $v_d\propto E$

Assume a conductor of

length $l$,

charge carrier density $n$,

drift velocity $v_d$,

cross sectional area $A$,

It is placed in an uniform electrical field ($E$)

current through the conductor ($i$) $=\frac{n\times l\times A\times q}{t}$

where $q$ is the charge of a carrier(electron) and $t$ is the time taken by carrier to pass through conductor

$\Rightarrow v_d=\frac{l}{t}$

$\Rightarrow i=n\times v_d\times A\times q$ .......(1)

so to obey ohm's law $i=\frac{V}{R}$ .....(2)

$R=\frac{\rho \times l}{A}$ ......(3)

$V=E\times l$ ....(4)

substituting (2),(3),(4) in (1):

$\Rightarrow n\times v_d\times A\times q=\frac{E\times A}{\rho }$

$\Rightarrow E=\rho \times n\times v_d\times q$

Thus $v_d\propto E$ . hence correct option is A