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Nodal analysis with dependent voltage source

  1. Dec 12, 2015 #1
    1. The problem statement, all variables and given/known data

    In attached image. Just curious as to how their nodal analysis is correct.

    2. Relevant equations

    ##I_{in} = I_{out}##

    3. The attempt at a solution

    Solution in image.

    I am just not sure how they applied nodal analysis here to find that ##I_s = \frac{12}{12} + \frac{12}{6} + \frac{12-8}{4}##. If I'm not mistaken, they are just finding V/R, correct? But isn't the voltage in ALL the resistors dependent in some way on both the 12 V source attached and also the dependent voltage source? Why does it seem like they only included the dependent voltage only on the 4-ohm resistor? Is their solution correct?
     

    Attached Files:

  2. jcsd
  3. Dec 12, 2015 #2

    gneill

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    Staff: Mentor

    Their solution is correct. If the applied independent source were changed to another value all the currents would be affected by the change, yet the resulting ratio of V/Is would turn out the same, yielding the same Rth.

    Perhaps you have some doubt about how the node equation itself was written?
     
  4. Dec 13, 2015 #3
    I guess I'm just not entirely understanding why the dependent voltage source is not considered in these equations for the other 2 resistors. Doesn't this voltage source affect the true voltage across the 6- and 12-ohm resistor, thus requiring this to be included when analyzing the current passing through these resistors? It seems to me that they are considering the voltage through the 6- and 12-ohm resistor to be simply 12 V, but that doesn't appear obvious to me since there is more than one voltage source in this entire circuit.
     
  5. Dec 13, 2015 #4

    gneill

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    Staff: Mentor

    The dependent source is not connected to the node where the 6 and 12 Ohm resistors connect; The external source is. So the external source must set their currents. Nothing can alter the potential difference imposed by a fixed voltage source and in this case the 12 V source is wired directly across those resistors.
     
  6. Dec 13, 2015 #5
    So referencing node b as 0, that makes perfect sense! I was blind, and now I see! :P Thanks!
     
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