The drift velocity of free electrons in a conductor is V, when a current. I is flowing in it If

step 1 For this question, we know that electric current i is equals to N -E A V -D. And so drift veloci

The drift velocity of free electrons in a conductor is V,...

The drift velocity of free electrons in a conductor is $\mathrm{V}$, when a current. $I$ is flowing in it If both the radius and current are doubled, then drift velocity will be.
(A) $(\mathrm{V} / 4)$
(B) $(\mathrm{V} / 2)$
(C) $4 \mathrm{~V}$
(D) $2 \mathrm{~V}$

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Key Concepts

Drift Velocity

Drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. It is commonly calculated using the relation I = nAeV, where I is the current, n is the charge density, A is the cross-sectional area, e is the charge of an electron, and V is the drift velocity.

Cross-Sectional Area Dependence on Radius

The cross-sectional area of a conductor is given by A = ?r², meaning that it is proportional to the square of the radius. Thus, any change in the radius affects the area quadratically. For instance, doubling the radius increases the area by a factor of four.

Relation Between Current, Drift Velocity, and Area

The relationship I = nAeV shows that for a fixed charge density and charge, drift velocity is directly proportional to the current and inversely proportional to the cross-sectional area. This means that if the current increases while the area increases by a greater factor, the drift velocity will adjust according to the ratio of these changes.

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