Ac analysis with dependent source

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Discussion Overview

The discussion revolves around analyzing an AC circuit that includes a dependent voltage source, an inductor, and a capacitor. Participants are attempting to determine the current I1 using mesh analysis and are addressing issues related to complex values, phase references, and sign conventions in their calculations.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents their calculations for I1 and expresses confusion over the discrepancy between their result and the expected answer.
  • Another participant suggests that the complex value for the independent voltage source is incorrect and mentions the relationship between cosine and sine functions.
  • A participant questions whether using the frequency domain with voltage as a zero phase reference affects the analysis.
  • Another participant agrees that using cosine as a reference is valid but notes that sign conventions must be carefully considered for inductors and capacitors.
  • There is a request for clarification on the calculations, particularly regarding the sign convention and the use of impedance for the capacitor in the participant's equations.
  • A participant points out a potential inconsistency in the frequency used in the calculations compared to the given voltage source frequency.

Areas of Agreement / Disagreement

Participants express differing views on the correct approach to the calculations, particularly regarding sign conventions and the interpretation of the voltage source. There is no consensus on the correct method or the validity of the calculations presented.

Contextual Notes

Participants highlight potential issues with assumptions about phase references and the definitions of circuit components, as well as discrepancies in frequency values that may affect the analysis.

craka
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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



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

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

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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.
 
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.
 
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?
 
Last edited:

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