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Applications of Linear Systems: Electrical Networks

  1. Feb 6, 2005 #1
    Hey,

    How do I find the current through the central resistor (the one that is 1 ohm) in this Wheatstone bridge attached to this post? What approach do I need to take here if I were to solve this using linear systems? Our professor poorly explained how electrical networks work. I can solve the linear system once I get it but I just need to figure out what I'm supposed to do in order to find those equations. Thanks.
     

    Attached Files:

  2. jcsd
  3. Feb 6, 2005 #2
  4. Feb 6, 2005 #3
    Try and redraw the circuit, but simplified so it's easier to see all the "routes" the current can go through. That really helps. :smile:
     
  5. Feb 6, 2005 #4
    Another way, without using the Kirchoff's laws, would consist of using the star-triangle transformations and compute in this way the electric potentials at the ends of the central resistor using only the Ohm's laws.
     
    Last edited: Feb 6, 2005
  6. Feb 7, 2005 #5
    See that's the thing, he never drew any arrows in the problem. I think he said something like we can make up our own directions but I really couldn't understand him. Would the final answer be the same no matter what the directions were?
     
  7. Feb 7, 2005 #6
    You can choose your own direction. If you have chosen your arrow in the 'wrong' direction, final answer will reflact that. In other words, you will get a negative result.
     
  8. Feb 7, 2005 #7
    OK here's a revised drawing of the diagram. I labeled the direction of the current this time. Are these directions fine? I know next to nothing about how current, voltage, and resistance work.
     

    Attached Files:

  9. Feb 7, 2005 #8
    Now mark the currents with some notations, say I, i, [tex]i_1[/tex].

    Say the current through the battory is I.

    So at the [tex]2 \Omega, 3\Omega[/tex] junction (left side in your recent picture) , let the current through [tex]3\Omega[/tex] is i and current through [tex]2\Omega[/tex] is I-i (Point rule).

    Do similarly at the 3,1,2 junction (top), assuming the current through [tex]1\Omega[/tex] is [tex]i_1[/tex]. Complete the current flow diagram by writing the currents through the other resistors. Don't introduce any other variables.

    You need only three variables namely I, i, [tex]i_1[/tex]. Apply Kirchoff's laws to get three equations to solve.

    Some one will be along with you if there is another easy way to do this.

    regards,
     
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