Derive the relation between electric current | vedclass

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(C) Let $v_d$ be the drift velocity,$n$ be the number of free electrons per unit volume,$l$ be the length of the conductor,and $A$ be the cross-sectio

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$I = neAv_d$

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(C) Let $v_d$ be the drift velocity,$n$ be the number of free electrons per unit volume,$l$ be the length of the conductor,and $A$ be the cross-sectional area of the conductor.The total number of free electrons in the conductor is given by $N = n(lA)$.The total charge $q$ contained in the conductor is $q = Ne = n(lA)e$.The time $t$ taken by the electrons to cross the length $l$ of the conductor with drift velocity $v_d$ is $t = l / v_d$.The electric current $I$ is defined as the rate of flow of charge: $I = q / t$.Substituting the values of $q$ and $t$,we get:$I = \frac{n(lA)e}{l / v_d} = neAv_d$.Thus,the relation is $I = neAv_d$.

Derive the relation between electric current and drift velocity.

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