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In the absence of applied potential, the electric current flowing through a metallic wire is zero because
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the electrons are drifted in random direction with a speed of the order of $10^{-2} \mathrm{~cm} / \mathrm{s}$
If there is no potential difference through a metallic wire, the current is zero because the electrons drift in a random direction with a speed of the order of $10^{-2} \mathrm{~cm} / \mathrm{s}$ so that the net charge crossing a particular cross-section in a given time is zero.
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