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Nodal-analysis to find voltage

  1. Feb 17, 2014 #1
    1. The problem statement, all variables and given/known data

    Use the node-voltage method to find v1 in the circuit(Figure 1) if i1 = 6.2A and i2 = 1.5A .
    Use the node-voltage method to find v2 in the circuit.

    Figure_P04.8.jpg

    2. Relevant equations

    G = 1/R

    QPFE3Hs.png

    3. The attempt at a solution

    Top side going from left to right, I assigned each node as 1, 3, then 2 (because of the way v_2 is assigned).

    For Node 1, I had:
    (v_1)/40 - (v_3)/8 = 6.2

    Node 3:
    -(v_1)/8 + (v_3)/80 = 0

    Node 2:
    (v_2)/120 = -1.5

    Solving, I got v_1 = -5.06 V and v_2 = -180 V. These are wrong (obviously). Any assistance would be appreciated.

    Moving image to bottom for visibility:

    Figure_P04.8.jpg
     
  2. jcsd
  3. Feb 17, 2014 #2

    BvU

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    Hello G and welcome to PF. Clear story. Do you have a reason to assign node 3, or could you make do with just nodes 1 and 2 ?
    Reason I ask is because V2 = V3 seems a reasonable assumption to me. (I will look up the thread where I made a complete fool of myself by completely missing such a thing -- fortunately others put me right...)

    Found it -- don't laugh!
     
  4. Feb 17, 2014 #3
    In that case where would I include the 80 Ohm resistor? Should it only be connected to v_2 on the equation?

    If so,
    Node 1:
    6.2 = (v_1)/40 - (v_2)/8
    -1.5 = (v_2)(1/80 + 1/120) - (v_1)/8

    Solving, v_1 = 3.86 V and v_2 = -48.8 V. Which is still incorrect.

    I'm out of attempts for solving for v_1, which I now know is 115 V.
     
  5. Feb 17, 2014 #4

    BvU

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    Ah, I interpret the node a equation a little different: after all, the 8 ohm is also connected to node a !
     
  6. Feb 17, 2014 #5
    Ah, I see now. I didn't realize I had to include the resistors between each node as also connected to it individually.

    1:
    6.2 = v_1 * (1/40+1/8) - v_2 / 8

    2:
    -1.5 = v_2 * (1/80 + 1/120 + 1/8) - v_1 / 8

    Ended with v_1 = 114.7 and v_2 = 88 (which is correct). Thanks.
     
  7. Feb 17, 2014 #6

    BvU

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    Always nice to have the answer at hand... I was still plodding :smile:
    And: you're welcome!
     
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