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From Wikipedia:

The drift velocity deals with the average velocity of a particle, such as an electron, due to an electric field. In general, an electron will propagate randomly in a conductor at the Fermi velocity.[5] Free electrons in a conductor follow a random path. Without the presence of an electric field, the electrons have no net velocity. When a DC voltage is applied, the electron drift velocity will increase in speed proportionally to the strength of the electric field. The drift velocity is on the order of millimeters per hour. AC voltages cause no net movement; the electrons oscillate back and forth in response to the alternating electric field (over a distance of a few micrometers

This can be found here

If AC voltages are causing no movement how is it that we can measure current, which is defined as - The net rate of flow of electric charge past a region.

What am I missing here? Thanks for your help.

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What am I missing here?

AC voltages cause no \$\color{red}{\boxed{\text{net}}}\$ movement.

You might have missed the red word above. It means average i.e. there is no long-term average movement but, of course, there is movement of charge for each half cycle of the applied AC waveform; one in one direction and the other in the reverse direction, averaging to zero.

If AC voltages are causing no movement how is it that we can measure current

AC is causing movement but no \$\color{red}{\boxed{\text{net}}}\$ movement.

Note to Neil: \$\require{cancel} \cancel{cancel}\$ works in answers

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  • \$\begingroup\$ That's a fun markup, red, boxed. Must use it some time. Where's the full list of these? \$\endgroup\$
    – Neil_UK
    Dec 9 '20 at 11:06
  • \$\begingroup\$ @Neil_UK dunno. I kind of stumbled across it when doing my crappy website. \$\endgroup\$
    – Andy aka
    Dec 9 '20 at 11:13
  • \$\begingroup\$ Thanks for your answer. Things are never this easy are they? \$\endgroup\$ Dec 9 '20 at 11:40
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    \$\begingroup\$ @ZhelyazkoGrudov you'll get used to it!! \$\endgroup\$
    – Andy aka
    Dec 9 '20 at 11:53
  • \$\begingroup\$ @Andyaka After a little searching, I've saved a file for myself with these links, mathjax markdown 1 markdown 2 \$\endgroup\$
    – Neil_UK
    Dec 9 '20 at 11:57
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If the wire was one atom thick, there would be a net migration of electrons in ac and DC, but the problem is scale.

1A is \$6.24 \times 10^{18}\$ electrons flowing in one second. That's a lot of electrons and as far as we are concerned, infinite.

But to allow those electrons to flow, looking at the cross sectional area of a wire, there must be significantly more copper atoms.

Copper has 29 electrons arranged in electron levels as: 2, 8, 18 and 1. That 1 electron in the valence shell accounts for the good conduction of copper. It is far (in atomic terms) from the nucleus and held by 1 proton. It can become a free electron with the application of little energy (heat, light, emf). The copper atom becomes a copper ion \$Cu^+\$, which will attract a free electron. The flow of electrons from atom to atom is current (net flow of electrons).

So individual electrons might only flow 𝜇m, the net flow is what matters. To get 1A of current to flow, \$6.24 \times 10^{18}\$ electrons must flow through the cross-sectional area of the wire in one second.

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