Transformers are strange and mysterious. Maybe somebody can drop some science on me.

Knowing ohm's law, I need to get my head together on this whole transformer thing. I know how transformers work, so you don't have to deal with that. I'm concerned with transformers as related to ohm's law. I have various questions, but where to start? Let me just start with one set of questions first.

If I have a transformer that's 120v in and 12v out, then I put a 3 amp load on the 12 volt side, it seems that I would have 36 watts and 4 ohms of resistance.

But wait a second - 120 volts is coming in to power things. Do I calculate my amps (3) based on 120 volts? If so, that would mean that I'm working with 360 watts, and 40 ohms of resistance. Is my amp load different on the 120 volt side, or does something in my resistance and my amperage change somehow between the 120v and the 12v sides? Does the 120v side "know" or "feel" the amperage load of the 12v side?

How do I deal with the discrepancy between the amperage on the output side of the transformer at 12 volts, and the input voltage, which changes all the numbers?

I understand that the resistance doesn't change, so this messes with my mind.

This is my first set of questions.

Upcoming: questions related to variac-controlled isolation transformer calculations regarding ohm's law.

Thanks for your help!