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Cornel19-Tanzanite
19-Tanzanite
April 8, 2024
Question

Electrical Engineering Challenge #2

  • April 8, 2024
  • 7 replies
  • 2873 views

Hello,

The problem is as following:
Find currents through R3 and R1 and voltages of R2, R1 and C1 in below circuit:

Cornel_5-1712569372845.png

Cornel_8-1712569562580.png


when:

a) 

Cornel_3-1712568938162.png

 


b) 

Cornel_2-1712568852677.png

    7 replies

    F
    Fred_Kohlhepp23-Emerald I
    23-Emerald I
    April 8, 2024

    Do you REALLY mean this: 

    Fred_Kohlhepp_0-1712576498984.png

    Or is mW to be megohms?

     

    C
    Cornel19-TanzaniteAuthor
    19-Tanzanite
    April 8, 2024

    Its ok as in yellow. Not megohms. 

    -
    -MFra-21-Topaz II
    21-Topaz II
    April 8, 2024

    Isn't there a switch right after the generator? Or, since it is not there, should we consider the circuit for an indeterminate time in such conditions, i.e. in the state in which the transient was completed? 

    C
    Cornel19-TanzaniteAuthor
    19-Tanzanite
    April 8, 2024

    In principle no, we should not consider that transient was completed.  You can try doing so If you want, but that will be not the complete solution. 

     

     

    L
    LucMeekes23-Emerald IV
    23-Emerald IV
    April 8, 2024

    What do you define as 'the voltage of R1'?

    L
    LucMeekes23-Emerald IV
    23-Emerald IV
    April 8, 2024

    Anyway, with V2 the voltage across R2 and V3 the voltage across C1, we get:

    LucMeekes_0-1712611800497.png

    gives:

    LucMeekes_2-1712611852152.png

    so:

    LucMeekes_3-1712611908845.png

    Now:

    LucMeekes_4-1712611954086.png

    so:

    LucMeekes_5-1712612016887.png

    And we find the time functions with:

    LucMeekes_6-1712612058710.png

    Enter component values and plot:

    LucMeekes_7-1712612111591.png

    When R1=200 mOhm:

    LucMeekes_8-1712612821621.png

     

    For case b:

    LucMeekes_11-1712613872261.png

     

    LucMeekes_12-1712613879894.png

     

    Following the same procedure as for case a:

    LucMeekes_13-1712613954357.png

    And with R1=200 mOhm:

    LucMeekes_14-1712614008055.png

    Success!
    Luc

     

     

     

     

    ttokoro
    21-Topaz I
    ttokoro21-Topaz I
    21-Topaz I
    April 9, 2024

    image.pngimage.pngimage.png

    t.t.
    C
    Cornel19-TanzaniteAuthor
    19-Tanzanite
    April 9, 2024

    Now, lets say that someone wants to express voltage across R2 to be function of voltage across C1 and current through L1/R3. Could give the desired equation for this?

    ttokoro
    21-Topaz I
    ttokoro21-Topaz I
    21-Topaz I
    April 11, 2024

    Using laplace we get same results by using IR3(s) and also by using VC1(s).

    image.pngimage.png

    But you want to express vR2(t) to be the function of vC1(t) and iR3(t). So the rest part of s regions of above are used to evaluate their time functions. They are include delta(t) function, therefore, some techniques are used evaluate the combolution integrals.

     

    image.png

    image.png

    image.pngimage.png

    image.png

    image.png

    Finally, we get the same results for all equations.

     

    image.png

    Second one is using digital convolution by * . At first digitize all signals of time domain. Also needs some treatment to the delta(t) function.

    image.png

    image.png

    image.pngimage.pngimage.png

    image.pngimage.pngimage.pngimage.png

    Finally, also get same results. So, this is the answers of your questions.

    image.png

    t.t.
    -
    -MFra-21-Topaz II
    21-Topaz II
    April 9, 2024

    Cornell 1.png

    Cornell 2.pngCornell 3.pngCornell 4.pngCornell 5.pngCornell 6.pngCornell 7.pngCornell 8.pngCornell 9.pngCornell 10.pngCornell 11.png

    -
    -MFra-21-Topaz II
    21-Topaz II
    April 11, 2024

    The network analysis (first case only) can also be done on the basis of the theory of network topology (see: Applied graph theory - W. K. Chen - North Holland ) and the formation of the TABLEAU for the node voltage method (see: Linear and non-Linear Circuits - L. O. Chua, C. A. Desoer, E. S. Kuh - Mc Graw Hill), see following photos:

    Cornell Top 1.pngCornell Top 2.pngCornell Top 3.pngCornell Top 4.pngCornell Top 5.pngCornell Top 6.pngCornell Top 7.pngCornell Top 8.pngCornell Top 9.pngCornell Top 10.pngCornell Top 11.pngCornell Top 12.pngCornell Top 13.pngCornell Top 14.pngCornell Top 15.png

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