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rvc

  • one year ago

Circuit question Please help :)

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  1. rvc
    • one year ago
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    |dw:1440434594670:dw|

  2. rvc
    • one year ago
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    @rishavraj @IrishBoy123 @mathmate @Michele_Laino @e.mccormick please help :)

  3. rvc
    • one year ago
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    |dw:1440434946834:dw|

  4. arindameducationusc
    • one year ago
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    wow... nice one.. i just had my dinner... was about to sleep.. would you mind if I do tomorrow morning?

  5. IrishBoy123
    • one year ago
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    i can have a try later today

  6. Michele_Laino
    • one year ago
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    I think that we have to apply the second and first principle of Kirchhoff

  7. rvc
    • one year ago
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    yep

  8. Michele_Laino
    • one year ago
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    |dw:1440436198619:dw| we have to suppose the existence of those currents, I1,...,I6

  9. rvc
    • one year ago
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    okay

  10. Michele_Laino
    • one year ago
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    now, we have to write the first principle of Kirchhoff at each node

  11. rvc
    • one year ago
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    incoming ccurrents= outgoing currents

  12. Michele_Laino
    • one year ago
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    yes! or algebraic sum of currents=0

  13. rvc
    • one year ago
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    yep

  14. Michele_Laino
    • one year ago
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    I label each node as below: |dw:1440436439762:dw|

  15. rvc
    • one year ago
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    oh okay

  16. Michele_Laino
    • one year ago
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    for node A: \[\Large {I_2} + 20 - {I_3} = 0\]

  17. Michele_Laino
    • one year ago
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    for node B: \[\Large {I_3} - {I_4} - 120 = 0\]

  18. Michele_Laino
    • one year ago
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    for node C: \[\Large {I_4} + 110 - {I_5} = 0\]

  19. Michele_Laino
    • one year ago
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    for node D \[\Large {I_5} - {I_6} - 60 = 0\]

  20. Michele_Laino
    • one year ago
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    for node Y: \[\Large {I_6} + 80 - {I_1} = 0\]

  21. rvc
    • one year ago
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    can we asume current through ab as I1 and ax as 20-I1 ?

  22. Michele_Laino
    • one year ago
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    for node X: \[\Large {I_1} - {I_2} - 30 = 0\]

  23. Michele_Laino
    • one year ago
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    with those equations, we have expressed the conservation of electrical charge

  24. Michele_Laino
    • one year ago
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    now, we have to happly the second principle of Kirchhoff, namely the subsequent equation for electrostatic field E: \[\Large \nabla \times {\mathbf{E}} = 0\] in order to do that we have to establish a positive sense into our circuit, like this: |dw:1440436999284:dw|

  25. Michele_Laino
    • one year ago
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    here is the missing equation: \[\large {V_{XY}} + 0.01{I_2} + 0.01{I_3} + 0.03{I_4} + 0.01{I_5} + 0.02{I_6} = 0\]

  26. Michele_Laino
    • one year ago
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    so, you have to determine all currents, I1,...,I6, then substituting into last equation, you will get the requested voltage drop Vxy

  27. Michele_Laino
    • one year ago
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    @rvc

  28. mathmate
    • one year ago
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    Hmm, There are 6 equations for 7 unknowns! @Michele_Laino I put 5 equations for the joints (the sixth is redundant) and the Kirchhoff's second law as 0.02*I1+0.01*I2+0.01*I3+0.03*I4+0.01*I5+0.02*I6=0 instead of using Vxy, and I seem to get satisfactory results, with I4 and I6 negative. Do you get the similar results? @rvc

  29. Michele_Laino
    • one year ago
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    if we collect all those equations above, we get the complete system as below: \[\Large \left\{ \begin{gathered} {I_2} + 20 - {I_3} = 0 \hfill \\ \hfill \\ {I_3} - {I_4} - 120 = 0 \hfill \\ \hfill \\ {I_4} + 110 - {I_5} = 0 \hfill \\ \hfill \\ {I_5} - {I_6} - 60 = 0 \hfill \\ \hfill \\ {I_6} + 80 - {I_1} = 0 \hfill \\ \hfill \\ {I_1} - {I_2} - 30 = 0 \hfill \\ \hfill \\ {V_{XY}}{\text{ }} + {\text{ }}0.01{I_2}{\text{ }} + {\text{ }}0.01{I_3}{\text{ }} + {\text{ }} \hfill \\ {\text{ + }}0.03{I_4}{\text{ }} + {\text{ }}0.01{I_5}{\text{ }} + {\text{ }}0.02{I_6}{\text{ }} = {\text{ }}0 \hfill \\ \end{gathered} \right.\]

  30. mathmate
    • one year ago
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    What I was saying is that there are 5 independent equations out of the first 6, so the last one will fill the void by expression Vxy as 0.02*I1. Then we get to have 6 equations, and 6 unknowns (I1 to I6).

  31. IrishBoy123
    • one year ago
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    yes, first 5 plus 0.02*I1+0.01*I2+0.01*I3+0.03*I4+0.01*I5+0.02*I6=0 gets there! [ 61. 31. 51. -69. 41. -19.]

  32. mathmate
    • one year ago
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    Yep, I got the same answers.

  33. mathmate
    • one year ago
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    Don't forget to find Vxy=61*0.02=1.22 V... etc.

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