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Ac analysis with dependent source

  • Thread starter craka
  • Start date
20
0
1. Homework Statement
Determine I1

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



2. Homework Equations
KVL & KCL


3. The Attempt at a Solution

[tex]
\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}
[/tex]

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
 

Attachments

220
0
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.
 
20
0
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.
 
220
0
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 capcitor 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?
 
Last edited:

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