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Kirchhoff's Rule and finding current with a system of equations

  1. Feb 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Using Kirchhoff's rules, calculate the current in R1 with the directions indicated in the figure above. Assume that R1 = 1.00kΩ, R2 = 3.00kΩ, R3 = 5.00kΩ, E1 = 75.0V, E2 = 65.0V and E3 = 85.0V.


    2. Relevant equations

    Kirchhoff's rules

    3. The attempt at a solution
    Using Kirchhoff's rules I can get I2 = I1 + I3. Which so far is the only thing I'm certain is correct. Next I need two equations from the loops (left and right) and then just solve the system of equations. I don't know if I am setting these up wrong but none of my answers have been correct thus far. I got:
    E1 - R1I1 - R2I2 - E2 = 0 and E2 - R2I2 - E2 - I3R3 = 0
    which come out to
    10 - I1 - 3(I2) = 0 and 20 - 3(I2) - 5(I3) = 0
    which results with I1 = 0.869 = 0.000869A when taking into account the resistances were kiloohms. Neither of these answers are correct. Calculations shouldn;t be the problems either because I've been lazy and just plugging into wolfram alpha to solve the systems of equations. I assume I am doing something wrong with equations 2 and 3. Any help would be appreciated.
     

    Attached Files:

  2. jcsd
  3. Feb 28, 2012 #2

    gneill

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    Staff: Mentor

    You may have slipped a sign somewhere or found the current assuming the opposite direction from that indicated. The magnitude of the value you found looks okay to me.
     
  4. Feb 28, 2012 #3
    thanks, apparently all the answers were just negative
     
  5. Feb 28, 2012 #4
    I thought I was done, but I have to calculate the potential between point c and f. I thought it would be E2 (65V) + I2R2 (-3.04mA*3kQ = -9.12V) = 55.9V. The parentheses there were just to clarify the values. This answer is not correct. What do I need to calculate the potential difference here, or do I just add them? If so, is there any easy way to keep track of these positives and negative which just seem to confuse things?
     
  6. Feb 29, 2012 #5

    gneill

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    Staff: Mentor

    They seem to be trying to trip you up with sign conventions! The reality is, current is flowing from node c towards node f (they have I2 pointing upwards). So the value you obtained for I2 is negative, right?

    So, proceeding from node f up through R2 there should be a voltage rise R2*|I2|. Then another rise as you go through E2. Now the question becomes, when they ask for the potential between c and f, do they want just the magnitude or are they implying a particular direction?
     
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