Ac analysis with dependent source

[craka]

Homework Statement

Determine I1

independent AC voltage source 10 cos 10^5t
inductor 60mH
capacitor 5nF
dependent voltage controlled voltage source 3Vx

Homework Equations

KVL & KCL

The Attempt at a Solution

$$\begin{array}{l} - 7.071 + 6000I_1 - j6000I_3 = 0 \\ I_3 = I_1 - I_2 \\ - 7.071 + 6000I_1 - j6000(I_1 - I_2 ) = 0 \\ j6000(I_1 - I_2 ) + 3v_x - j2000 = 0 \\ v_x = 6000I_1 \\ - 7.071 + 6000I_1 - j6000(I_1 - I_2 ) = 0 \\ j6000(I_1 - I_2 ) + 3(6000I_1 ) - j2000 = 0 \\ 24000I_1 = 7.071 + j2000 \\ I_1 = (2.94625 \times 10^{ - 4} ) + j0.083333 \\ I_1 = 0.0833\angle 89.79^o \\ \end{array}$$

The answer for I1 is given as 0.33mA @ 171.9 degrees

Could someone help me here please, gone over this for a couple hours still stumped.
Cheers

 

[Kruum]

Quickly going through your attempt, all I can spot is that your complex value for the independent supply is incorrect. cos(x)=sin(x+pi/2)...

One sure-fire way to get it is to use mesh method.

 

[craka]

If I convert to the frequency domain and have my voltage as my zero phase reference it shouldn't matter should it? ie voltage 7.071 V @ 0degrees

I thought what I tried was mesh loop analysis.

 

[Kruum]

Yes, of course you can calculate it as cos as the reference. But in that case you need to start playing with the signs a bit more due to the definition of inductor and capacitor.

And by mesh method I meant using the matrix form. You only get 2x2 matrix, which is easy to deal with.

Edit: Going more in-depth to your calculations, looks like your sign convention differs from mine. Can you explain the method how you got rows 1 and 4? Especially in row 4 why do you only use the impedance of the capacitor or is it a typo? And is the voltage source given as 10cos(10^5t), because in the picture the frequency is 15.9kHz, which would give w=31831pi?