Question

For which of the following dependence of drift velocity $V_d$ on electric field $E$ is Ohm's law obeyed ?

​​​​​​​$[$1 Mark$]$

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

Answer 1

The correct option is A $V_d\propto E$

Drift velocity, $V_d=\frac{I}{nAe}\dots \left(1\right)$

from ohm's law

$V=IR=I\left(\frac{\rho l}{A}\right)\dots \left(2\right)$

and $V=El\dots \left(3\right)$

from $\left(2\right)$ and $\left(3\right)$

$E=I\frac{\rho }{A}$

$\Rightarrow \frac{I}{A}=\frac{E}{\rho }\dots \left(4\right)$

Putting value of $\frac{I}{A}$ in $\left(1\right)$

$V_d=\frac{E}{n\rho e}$

$\Rightarrow V_d\propto E$