Finding Node Voltages Using the Node Method

  1. 1. The problem statement, all variables and given/known data

    Find the node voltages for the circuit shown.

    2. Relevant equations

    See attachment.

    3. The attempt at a solution

    I have chosen my ground node as the set of nodes in the bottom of the image and labeled all of my unknown voltages as en.

    Here is what I have so far. Where G = 1/R

    For the node labeled e1:

    (e1-v0)G1 + e1(G3) + (e1-e2)I1 + (e1-e2)G2=0

    For the node labeled e2:

    (e2-e1)(-I2) + e2(G4) + (e2-e1)G2=0

    I am pretty sure my problem lies in the way I am handling the currents in the node. I started plugging in numbers after I simplified it all and one of my unknown voltages went away. After that I looked at it again and knew I was doing it wrong. Most of the examples in the book don't deal with a current parallel to a resistor.

    I think the way I should have done it is rather than subtracting voltages and multiplying like I am doing with the resistor nodes, is just take the current by itself.

    So in my above equation e1)(-I1) would just become -I1 since I am not using ohms law for current. I think I only need current? Does that sound better?
     

    Attached Files:

  2. jcsd
  3. gneill

    Staff: Mentor

    Yup. Much better. Voltage x current yields power, not a current, so is quite unsuitable for a KCL expression!
     
  4. Perfect! Thanks for the help.

    It seems half the time I post problems, I get them mostly figured out just typing the post up. :)
     
  5. gneill

    Staff: Mentor

    Yup. Typing it out so that it make sense to someone else can often help one re-evaluate one's logic and assumptions. :smile:
     
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