Hey guys, I have a question about transformer. So when you step up the voltage in the secondary wire, the current goes down because power stays the same (from the equation P=VI) but since the resistance of the wire is constant, when voltage increases, shouldn't the current increase as well because of ohms law? (V=IR)

When you say "voltage increases so current decreases," you're assuming that P is fixed, whereas when you say "voltage increase, current increases" you're assuming R is fixed. But in fact, it isn't possible to change the current while keeping both of these things constant.

Let us assume that we're actually keeping R fixed, i.e. we're working with a normal transformer. Using V=IR, and P=IV. Substituting the first into the second, we have that P=I^2R. So if you double the current, the power will increase by a factor of four.

So for a transformer, the power doesn't stay constant, and that's why the current goes down with voltage.