Current and drift velocity in a conductor are related by the equation:

$\overline{){\mathbf{i}}{\mathbf{=}}{\mathbf{n}}{\mathbf{A}}{\mathbf{e}}{{\mathbf{v}}}_{{\mathbf{d}}}}$

Free electrons through the wire produce a current that can be expressed as:

$\overline{){\mathbf{i}}{\mathbf{=}}\frac{\mathbf{N}\mathbf{e}}{\mathbf{t}}}$, where N is the number of free electrons through the wire.

Comparing the two equations, we solve for t as follows:

$\begin{array}{rcl}\frac{\mathbf{Ne}}{\mathbf{t}}& \mathbf{=}& \mathbf{n}\mathbf{A}\mathbf{e}{\mathbf{v}}_{\mathbf{d}}\\ \mathbf{t}& \mathbf{=}& \frac{\mathbf{N}\overline{)\mathbf{e}}}{\mathbf{nA}\overline{)\mathbf{e}}{\mathbf{v}}_{\mathbf{d}}}\\ & \mathbf{=}& \frac{\mathbf{N}}{\mathbf{n}\mathbf{A}{\mathbf{v}}_{\mathbf{d}}}\end{array}$

The electron drift speed in a 3.00-mm diameter gold wire is 5.00×10^{-5} m/s. How long does it take 1 mole of electrons to flow through a cross section of the wire?

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