What causes an electric current in a wire?

Well let's analyse.

First we know Ohm's law of resistance that states:

Where R is resistance, U is voltage and I is current.

If we express current we get:

Because resistance cannot be equal to 0 (violation of mathematical law) the only thing that may cause current being zero is voltage.

Which means that as long as your voltage is bigger than 0V then there will be current (if we are talking about AC).

So to answer the question: Electric current is caused by voltage and regulated by resistance.

Hope this helps.

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