For which of the following dependencies of dr | vedclass

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(A) Ohm's law states that the current $I$ flowing through a conductor is directly proportional to the potential difference $V$ applied across its ends

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$v_d \propto E$

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(A) Ohm's law states that the current $I$ flowing through a conductor is directly proportional to the potential difference $V$ applied across its ends,provided the physical conditions remain constant. This implies that the current density $J$ is directly proportional to the electric field $E$ $(J = \sigma E)$.Since the current density is given by $J = n e v_d$,where $n$ is the number density of electrons,$e$ is the charge of an electron,and $v_d$ is the drift velocity,we have $n e v_d = \sigma E$.This implies $v_d \propto E$.Therefore,Ohm's law is obeyed when the drift velocity is directly proportional to the electric field.

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

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