For the case of an ideal transformer, I understand that the voltages are proportional to the turns ratio.

$$\frac{V_1}{V_2}=\frac{N_1}{N_2}$$

since I assumed the transformer to be ideal:

$$V_1I_1=V_2I_2$$

so it follows that

$$\frac{V_1}{V_2}=\frac{N_1}{N_2}=\frac{I_2}{I_1}$$ -------(1)

So, from this equation it seems that the values of currents are related to the turns ratio.

But some confusion popped out when I apply Ohm's law in transformer (which I am not sure if I can use Ohm's law here)

If we can apply Ohm's law, we have $$V_1=I_1R_1$$ for primary coil and $$V_2=I_2R_2$$ for secondary coil and we can write from equation (1):

$$\frac{I_1R_1}{I_2R_2}=\frac{N_1}{N_2}$$

From this equation, the currents in both coils are dependent on the resistance. While the voltages must depend on the turns ratio, I think the current should depend on the external circuit the coil connected with. So, I am confused that whether equation (1) is true.

The relationship between the currents doesn't come from applying Ohm's law to the coils in the transformer.

Suppose we have the transformer connected to some input voltage on the primary side and some load on the secondary side:

We connect our transformer to some load $$R$$ so a current $$I_s$$ flows in the secondary. The voltage across the load is $$V_s$$ and the current through the load is $$I_s$$ so the power being delivered to the load is:

$$P_s = V_s I_s$$

Now look at the primary coil. We are applying a voltage $$V_p$$ to it and the current through the primary is $$I_p$$ so the power being delivered to the primary coil is:

$$P_p = V_p I_p$$

But assuming an ideal transformer the power being delivered to the primary coil must be the same as the power being delivered to the load otherwise energy wouldn't be conserved. That means the two powers must be the same and therefore:

$$V_p I_p = V_sI_s$$

And there is your expression relating the currents to the voltages. But it has come from conservation of energy not Ohm's law.

• But is it okay to apply Ohm's law to the load? If is, we have $V_S=I_SR$. But if the secondary current is determined by the transformer, it should not be affected by the resistance of the load. Commented Sep 30, 2020 at 13:27
• The secondary current is determined by the load, and the secondary current determines the primary current. The secondary current tries to change the flux in the core of the transformer, but to maintain the voltages the flux must stay the same. The primary current must change to keep the flux magnitude constant. Commented Sep 30, 2020 at 13:48