In transformers, the ratio of the voltages equals the ratio of the turns - so double the output coil's turns and the output voltage doubles. Then, in order to conserve energy, current halves.
This makes perfect sense in terms of P=VI, but what happened to V=IR? Doubling voltage and halving the current seems to completely contradict this basic law. That is, of course, unless the resistance in the output circuit changes, with R proportional to V^2 - but I don't see how this is possible.
So how can a transformer obey both laws? Can resistance change or am I missing something else?