What is the effective value of the current of the voltage generator?

I need help with this task, if anyone had a similar problem it would help me.

A voltage generator is connected to the primary of an ideal transformer, transformation ratio n rms values ​​of the electromotive force U and the circular frequency ω, and is bound to the secondary complex impedance receiver Z, as shown in the figure. What is the effective value of the current of the voltage generator, if the receiver (a) is a resistance resistor R, (b) capacitance capacitor C and (c) inductor L? I do:

$$\frac{U_1}{U_2}=\frac{N_1}{N_2}\\I_2=\frac{U_2}{Z}$$

It follows from this:

$$U_2=\frac{U_1N_2}{N_1}\\I_2=\frac{U_2}{Z}$$ From this we have further: $$I_2=\frac{U_1N_2}{ZN_1}$$ Further: $$\frac{I_1}{I_2}=\frac{N_2}{N_1}\rightarrow I_1=\frac{U_1N_2}{ZN_1}\cdot\frac{N_2}{N_1}\rightarrow\frac{U_1}{Z}\cdot \frac{N_2^{2}}{N_1^2}$$

$$a)\ I_1=\frac{U_1}{R}\left(\frac{N_2}{N_1}\right)^2\\ b) \ I_1=U_1jwC\left(\frac{N_2}{N_1}\right)^2\\ c)\ I_1=\frac{U_1}{jwL}\left(\frac{N_2}{N_1}\right)^2$$

Is that correct ?

• Ideal transformers transform impedance by $N^2$. Nothing else to say or prove. Jun 9 '21 at 11:09