A gold wire and an aluminum wire have the same dimensions...

A gold wire and an aluminum wire have the same dimensions and carry the same current. The electron density (in electrons/cm $^{3}$ ) in aluminum is three times larger than the density in gold. How do the drift speeds of the electrons in the two wires, $v_{\mathrm{Au}}$ and $v_{\mathrm{Al}},$ compare?

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Key Concepts

Current–Drift Velocity Relationship

This concept centers on the relationship I = n × q × v?d? × A, where I is the electric current, n is the charge carrier density, q is the charge per carrier, v?d? is the drift velocity, and A is the cross-sectional area. It shows that, for a fixed current and wire dimensions, the average drift velocity of the carriers is inversely proportional to their density.

Drift Velocity

Drift velocity is the average speed at which electrons move through a conductor when an electric field is applied. In conductors carrying a constant current, if the number of electrons per unit volume increases, each individual electron must move more slowly to maintain the same total current.

Charge Carrier Density

The charge carrier density is the number of free charge carriers (like electrons) per unit volume in a material. It affects how current is distributed in a conductor; a higher density means more electrons are available to share the conduction, thus requiring a lower drift velocity to carry a given current.

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