In a stepped-up transformer, why does input power equal to output power even though voltage is increased? I just learned about the basics of transformers. I am aware that according to the law of energy conservation, power input should be equal to power output. However, when I think about this with ohm's law, in the secondary coil, power remains the same but voltage is increased implies resistance is somehow increased. But what causes this "increase in resistance"? I looked through some of the previous posts on this topic but I think all of them don't explicitly explain this increase in resistance. Maybe there is some more advanced stuff that is not covered in our high-school syllabus, but I want to know more. Thanks in advance!
 A: 
but I want to know will the  in the secondary coil change when the
turn ratio of the transformer changes? If yes, why?

The $R$ of the secondary coil will not change because the $R$ for the primary and secondary coils is zero for an ideal transformer in which power in equals power out. If they had any resistance, some energy would dissipated as heat and therefore not be available to a load connected to the secondary.

but then according to $P=\frac{V^2}{R}$, when the power is step-up(or
down), the power will change. What is wrong with this argument?

If the secondary voltage is greater than the primary voltage, then  the primary current has to be greater than the secondary current since
$$\frac{V_{p}}{V_{s}}=\frac{I_{s}}{I_{p}}$$
In other words, the power will change for both the primary and the secondary
Hope this helps.
A: You have $P_1=P_2$, or $V_1^2/R_1=V_2^2/R_2$,  where $R_1$ is the apparent resistance of the primary circuit. If you change $R_2$ you are changing both, the power and the apparent resistance $R_1$ ("apparent" because is not linked to any actual resistance), but not the voltages.
