Phase Difference?(Mutual Inductor)

[genxium]

Homework Statement

For a mutual inductor component like this, <C1,L1> is resonant to f0, <C2,L2> is also resonant to f0 too, and the mutual inductance between L1 and L2 is M, and M is very small so that it could be ignored in approximation. Assume that the voltage Vin on <C1,L1> is the induced voltage from sinusoid wireless signal, the current going through L1 is i1, and the current going through C2 and L2 is i2, find the phase different between i1 and i2.

Homework Equations

$\Phi_{12} = M \cdot i_1 , Emf= - \frac {d \Phi}{d t}$

The Attempt at a Solution

Assume $i_1=Ae^{j \omega_0 t}, \omega_0 = 2 \pi f_0,$then $E_2= -j \omega_0 M i_1,$, <C2,L2> forms a serial connection , so I assume that $i_2$ is in phase with $E_2$, then the phase difference is $\frac{\pi}{2}$, but I'm not sure about the assumption "$i_2$ is in phase with $E_2$", cause $\omega_0$ makes $j \omega_0 L_2+\frac{1}{j \omega_0 C_2}=0$, could I say that $E_2,i_2$ is "almost in phase" for this case?

 

[_coyote_]

Yes, you can say that they are "almost in phase" since the impedance of <C2,L2> is zero at f0. The mutual inductance M will not affect the phase relationship between E2 and i2 significantly.