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In an alternating current, the flow of electric charge periodically reverses direction, and the number of times it does that is called the frequency of the current. However, if the frequency of an AC is made infinite, would any current flow? I asked this question to my school teacher and he was unable to provide me with an answer unfortunately.

If I consider a horizontal wire, through which an AC is flowing, then I can say that an electron in the wire is moving 50 times left and 50 times right, if the frequency is assumed to be 50Hz. It seems to me that if I increase the frequency, the displacement of the electrons in both the directions, that is left and right, will gradually decrease, and finally become 0, when frequency is infinite, thus making I = 0.

What have I got wrong?

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You are correct, but probably not for the reason you think.

At low frequencies the inertia of the electrons is small enough to be ignored, that is we assume that when we apply a voltage the electrons instantaneously accelerate to their steady state velocity. As you increase the frequency of the applied voltage the inertia of the electrons starts to become significant, and above a frequency called the plasma frequency the electrons can no longer move fast enough to respond.

For most metals the plasma frequency is around or slightly below that of visible light.

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