When current flowing through a conductor is I, average drift...

When current flowing through a conductor is I, average drift velocity of free electrons is $\mathrm{V}_{\mathrm{d}}$. Now when $6 \mathrm{I}$ current is flowing through a conductor having 3 times cross sectional are of same material what will be average drift velocity of free electrons? (A) $2 \mathrm{~V}_{\mathrm{d}}$ (B) $\left(\mathrm{V}_{\mathrm{d}} / 2\right)$ (C) $3 \mathrm{~V}_{\mathrm{d}}$ (D) $18 \mathrm{~V}_{\mathrm{d}}$

When current flowing through a conductor is I, average drift velocity of free electrons is $\mathrm{V}_{\mathrm{d}}$. Now when $6 \mathrm{I}$ current is flowing through a conductor having 3 times cross sectional are of same material what will be average drift velocity of free electrons?
(A) $2 \mathrm{~V}_{\mathrm{d}}$
(B) $\left(\mathrm{V}_{\mathrm{d}} / 2\right)$
(C) $3 \mathrm{~V}_{\mathrm{d}}$
(D) $18 \mathrm{~V}_{\mathrm{d}}$

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Key Concepts

Drift Velocity

Drift velocity is the average velocity at which free charge carriers, such as electrons, move through a conductive material when subjected to an electric field. It is a crucial microscopic parameter that connects the behavior of individual charge carriers with the macroscopic current observed in a circuit.

Current Density

Current density is defined as the current per unit cross-sectional area through which the current flows. It serves as a bridge between the macroscopic quantity of current and the microscopic properties of the charge carriers, linking directly to the drift velocity through the relation J = nqv?d?, where n is the charge carrier density and q is the charge of each carrier.

Relationship between Current, Drift Velocity, and Conductor Cross-Sectional Area

The relationship is given by the equation I = nqAv?d?, which shows that the current (I) is proportional to the number density of charge carriers (n), the charge (q), the cross-sectional area (A), and the drift velocity (v?d?). This relation is pivotal in understanding how changes to the current or the cross-sectional area of a conductor impact the average drift velocity of the free electrons.

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