I understand how to use a transformer in practice, and I know that transformers obey the law of conservation of energy, but I'm confused as to how step-up and step-down transformers obey Ohm's law and KVL. This is an example of why I get confused given my current understanding of electricity:
Say there's an ideal step-down transformer that converts 10V at 1A to 1V at 10A, and the secondary of the transformer has a 0.1Ω load across it. According to KVL, there should be 1V dropped across the load because the secondary produces 1V, and because the current is the same everywhere in a series circuit, there should be 10A through the load. Ohm's law holds because the 1V dropped across the load is equal to the 10A through the load times the 0.1Ω resistance of the load. But if you replace the load with a different resistance one, how does Ohm's law hold? Based on my current knowledge, there would still be 1V dropped across the resistor and 10A through it, but V ≠ IR.
I know that something has to be wrong with my current understanding, but I'm not sure what. Does the current through the secondary change when you change the load? Does the voltage across it change? Is the current through the secondary not equal to the current through the series load? Or does it cause a change in the current/voltage through/across the primary? I've been trying to think of an answer to this question myself and I've gone back and re-read a lot of material on inductors and transformers but I still can't figure it out, so if anyone thinks they have a good explanation, I would really appreciate it. Thank you!