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I found online that Ohm's law still applies to an AC circuit and that $V_{peak} = RI_{peak}$. However, I can't seem to find anywhere weather an AC source will :

  • Act as a voltage source and keep its peak (and average) voltage constant when we change resistance or
  • Act as a current source and keep its peak (and average) current constant when we change resistance

Which one is it? Do both types of sources exist, and if not, why not?

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It depends on what you have. Sources can be modeled as a current source or a voltage source. If you treat it as a voltage source, it will always output that peak voltage and the circuit current will change according to the resistance changes. If you treat it as a current source, it will always output that peak current and the voltage drop across it will change according to the resistance changes. Now, I don't know if the $R$ you have provided is internal resistance or equivalent circuit resistance. If it is the internal resistance of the source you can use it to flip back and forth from current source to voltage source. The voltage source will be in series with its internal resistance, and the current source will be parallel to it. In any way, you cannot analyze it as both a current source and a voltage source (as far as I know).

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