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Resistors and kirchoff's law

  1. Oct 26, 2008 #1
    What is the current through the 10 ohm resistor? See figure below.

    The equations I got were:

    But I am confused as to how to get the last equation from the junction. Would it be I1 +I2=I3?

    Once you have the three equations you would combine them and solve for I2, right?

    Thanks. I appreciate the help.


    Attached Files:

  2. jcsd
  3. Oct 26, 2008 #2
    Yes, you are correct. Using the loop rule will give you two independent equations and the junction rule will give you a third. Then you have 3 equations with 3 unknowns.
  4. Oct 26, 2008 #3


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    Yes, that is correct ... except that the sign of your currents should reflect the proper direction in which you took the loop equations.
  5. Oct 26, 2008 #4
    So would the third equation be:
    I3=I1 + I2
  6. Oct 26, 2008 #5


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    What are the directions of I1, I2, and I3?
  7. Oct 26, 2008 #6
    My professor said they can be anything as long as they are not all three the same. I did one going in a two going out, downward toward R3 and sideways toward R2.

    So is my equation correct? If not why?And how did you decide?
  8. Oct 26, 2008 #7


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    The best way I find is to visualize a flow - clockwise or reversed - that doesn't really matter except of course in how you treat voltage sources that you encounter in your loop.

    Having defined your flows, then along those paths that the currents conjoin, treat them plus or minus with the same sign as in the way that you have taken them in the loops of the loop equations.
  9. Oct 26, 2008 #8
    well doesnt my last equation shows the directions, downward + sideways= inward flow or I3+I2=I1?????

    If not; need more directions.
  10. Oct 26, 2008 #9


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    Yes, they can be anything, but once you decide what they are you must be consistent. And I suspect you are not being consistent, from the equations you wrote.

    I don't understand any of this. There is no R2 or R3 in your circuit diagram!

    So let me explain my question in more detail:

    1. From the voltage equations you wrote in Post #1, it's pretty clear that I1 is the current going through the 12V source and 5-ohm resistor at the top of the circuit. Question: does a positive I1 indicate current going to the right or left there?

    2. Likewise, you are using I2 for the current through the 10-ohm resistor in the middle. Would a positive value of I2 mean the current goes to the right or left through that resistor?

    3. And I3 is the current through the 9V source and bottom 5-ohm resistor. Would a positive I3 go to the right or left through those components?

    If you can answer those questions, I could tell you if I1=I2+I3, and I could also tell you which of your two voltage equations is wrong.
  11. Oct 26, 2008 #10
    according to my professor those two equations are correct. R2= 10 ohm R1=5 ohm and R3= other 5 ohm. I1 = left I3= right I2 is the one I am not too sure about. If the equations are not right, please explain, so I can let my professor know and so I can learn how to solve this problem correctly. And how do you find the third equation. And explain about the current going through R2 and the junction.
  12. Oct 27, 2008 #11


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    If I2 is to the left, then the 1st equation is wrong.
    If I2 is to the right, then the 2nd equation is wrong.
    (If you tell your professor this, I'm sure he will agree. :smile:)

    Since the I2 direction is not specified in the problem statement, you the problem solver may choose its direction. In fact, you are required to choose a direction for it in order to solve the problem. Until you do that, we cannot tell you whether I1=I2+I3 or I3=I1+I2.
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