# Does resistance in second circuit changes in transformed circuit?

Let $V_1$, $I_1$, $R_1$ and $V_2$, $I_2$, $R_2$ be voltages, currents, resistance in first, second circuit.

And we assume $R_1=R_2$, $I_1\neq I_2$.

The conservation of electrical power $P=V_1I_1=V_2I_2$ holds in the transformer circuits.

Hence $I_1^2R_1=I_2^2R_2$, $R_2=(I_1^2/I_2^2)R_1$ which leads to a contradiction.

What am I missing?

What you're missing is a source that's driving the whole thing. As you wrote it, there's no contradiction: $I_1=I_2=0$. With a source included, it's no longer true that $I_1^2R_1 = I_2^2 R_2$.
If $R_1=R_2$, then also $I_1=I_2$ (assuming no losses, and so on). Your simple argument is a "proof by contradiction" of this simple assertion.