Nodal analysis help

Discussion in 'Homework Help' started by yuxytet34, Mar 29, 2015.

  1. yuxytet34

    Thread Starter New Member

    Mar 29, 2015
    5
    0
    Im having trouble finding expressions for the currents I7, I2, I3, I6. Could anyone please help me out with this?
    The three nodes are K1, K2, K3 which are placed at the same positions as V1,V2,V3, the voltages we want to find.
    Ive used Kirchhoffs law to label the incoming and outgoing currents at every node. BTW, I1=9A, I2=4A and R1,3,5,6,7,8=2Ω and R2,4,9=4Ω.
    I have I3=V1/R9, I4=V1-V2/R2 , I5=V1/R6\\R1 I6=really not sure. I7=not sure here either I8=V3/R5
    I9=V3-V2/R4. I then want to make a matrix out of it and solve it through Cramers rule. That part though Im pretty sure I can deal with. Its getting the right matrix that troubles me.

    Thanks in advance!!
    And sorry for all the scribbling on the diagram.
     
  2. WBahn

    Moderator

    Mar 31, 2012
    17,720
    4,788
    How have you used Kirchhoff's Law to label the currents? Labeling currents is an arbitrary decision made separate from Kirchhoff's Laws.

    It looks like you done everything up to the point of actually applying Kirchhoff's Current Law at each node. Try doing that and see what you get.
     
  3. yuxytet34

    Thread Starter New Member

    Mar 29, 2015
    5
    0
    I believe I have, its finding expressions for a few of those currents that confuses me.
     
  4. WBahn

    Moderator

    Mar 31, 2012
    17,720
    4,788
    If you have applied Kirchhoff's Current Law (KCL), then please show the equations that resulted from doing so. There should be three, one each by applying KCL at nodes V1, V2, and V3.

    You have labeled ten currents. Which few are confusing you as far as finding expressions for them? It might help to make a table of them; if nothing else, it will make it a LOT easier for those of us trying to help you. Pulling the bits and pieces from your first post, I get

    I1 = 9A
    I2 = 4A
    I3 = V1/R9 ( WRONG )
    I4 = V1 - V2/R2 ( Technically wrong -- needs to be (V1-V2)/R2 )
    I5 = V1/R6\\R1 ( Better written as V1/(R6||R1) )
    I6 = really not sure
    I7 = not sure here
    I8 = V3/R5
    I9 = V3-V2/R4 ( Technically wrong -- needs to be (V3-V2)/R4 )
    I10 = (not mentioned)

    You need to be more careful about order of operations (I4 and I9), remember, multiplication/division before addition/subtraction. Don't rely on people inferring what you meant to write. Keep in mind that you are going to be putting expressions like this into computer programs, spreadsheets, simulators, etc. and they will NOT infer what you meant to write, they will evaluate what you actually write. If you continue to be sloppy with your expressions, then you will be just as sloppy when you enter expressions into those programs. Get in the habit of writing what you mean to say correctly -- it will save you hours of grief down the road.

    In looking over the current you got and the ones you didn't, it's hard to understand where your problems are coming from. By this I mean that you have one current that you get correct and then another conceptually identical current that you either get wrong or don't know how to do. Perhaps pointing those out will make something click.

    I6 and I8 are conceptually identical. Each is connected between V3 and ground (0V). So why are you able to get the expression for I8 but can't for I6?

    I3, I4, and I9 are conceptually identical. Aside from the order of operations already noted, you got I4 and I9 just fine. Why is I3 different?

    As for I10, I think you just overlooked it. Do you see how a clear, organized table helps ensure that you don't overlook things?
     
  5. yuxytet34

    Thread Starter New Member

    Mar 29, 2015
    5
    0
    Yeah, I know I was in a real rush when I was writing it down, I usually dont make those mistakes. Sorry about that though :S. Anyhow, I10 i forgot to jot down as well. I10 would be V2/R3||R7.
    Also I dont know how I would make a table here and I didnt really have the time. Anyhow I6, I7 although Im still not really sure, Id say I6=(V1-V3)/R8 and I7=(V1-V3)/R5||R8. I3 would then also be (V1-V3)/R9. Although I could make an expression for I7 by taking into account that I3+I2=I7+I6. By pure observation though Im not sure if what I wrote is right.
     
  6. WBahn

    Moderator

    Mar 31, 2012
    17,720
    4,788
    A table doesn't have to be anything fancy. Notice that the table in my post is nothing more than a list of the currents and what they are equal to. But by putting them in order and in a consistent format and one per line it makes them very easy to look at evaluate. Must easier than embedding equations in the text.

    Anyhow I6, I7 although Im still not really sure, Id say I6=(V1-V3)/R8 and I7=(V1-V3)/R5||R8. I3 would then also be (V1-V3)/R9. Although I could make an expression for I7 by taking into account that I3+I2=I7+I6. By pure observation though Im not sure if what I wrote is right.[/QUOTE]

    I think part of the problem is that you may not truly comprehend what a "node" is. You seem to recognize that the voltage at the top of R5 is V3 but yet do not recognize that the voltage at the top of R8 is also V3.


    KCL9.png

    There are exactly four nodes in this circuit. A red node (V1), a blue node (V2), a green node (V3) and a black node (GND or 0V).

    I6 is the current downward flowing through R8.

    Ohm's Law says that the current flowing through a resistor is the difference between the node that the current is flowing from and the node that the current is flowing to divided by the resistance.

    I6 = [ (voltage on the green node) - (voltage on the black node) ] / R8
     
  7. yuxytet34

    Thread Starter New Member

    Mar 29, 2015
    5
    0
    Yep you were right, I didnt 100% understand it. Great explanation through the diagram!! Thanks mate.
     
  8. WBahn

    Moderator

    Mar 31, 2012
    17,720
    4,788
    Thanks.

    Even today there are times when I will get out a pen/pencil and highlight the nodes in some way in order to really see what is connected to what. It's too easy for the human mind to make inferences that aren't really there.
     
Loading...