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Finding potential at certain points in circuit

  1. Mar 29, 2008 #1
    [SOLVED] Finding potential at certain points in circuit

    1. The problem statement, all variables and given/known data
    Calculate the potential of [tex]V_1[/tex] and [tex]V_2[/tex]

    See attached circuit configuration (circuit2.gif)


    2. Relevant equations
    Ohms law: U = RI
    Kirchhoff's laws


    3. The attempt at a solution
    I tried to solve it with superposition but my teacher says I've got the wrong sign for [tex]V_2[/tex].
    No matter how I try, I get a positive potential for [tex]V_2[/tex].

    I've attached my solution (solution.jpg)

    Any suggestions?
     

    Attached Files:

  2. jcsd
  3. Apr 3, 2008 #2
    I think I've found a solution to this problem, but I'm still not convinced about how the currents flow in this circuit configuration.

    My solution:
    Point 1 obviously has the potential 7V. The node beneath the 15 ohm resistance, which I call [tex]V_3[/tex], has the potential -6V.
    The voltage over the 15 ohm resistance is [tex]u_3 = V_2 - V_3[/tex].
    But we also have
    [tex]u_3 = \frac{15 \Omega}{10 \Omega + 15 \Omega + 25 \Omega} 10V = \frac{150}{50}V = 3V[/tex]

    And finally
    [tex]V_2 = u_3 + V_3 = 3 + (-6) V = -3 V[/tex]

    Could somebody verify this for me?
     
  4. Apr 3, 2008 #3

    Tom Mattson

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    You don't need to know a priori what the current directions are. Just assume a direction for the current in each loop. If you're wrong, then you'll pick up a minus sign. No worries.

    I got -3V too, but I did it by Mesh Current Analysis (which is pretty easy in this problem, as each mesh equation only has one variable).
     
  5. Apr 3, 2008 #4
    I'm curious about how you used mesh current analysis in this problem. Would you mind describing it to me?
     
    Last edited: Apr 3, 2008
  6. Apr 3, 2008 #5

    Tom Mattson

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    Assume a direction for each mesh current. I called the current in the left mesh [itex]i_1[/itex] and took it to be clockwise, consistent with the voltage source in that loop. Similarly I called the current in the right mesh [itex]i_2[/itex] and took it to be counterclockwise. Then I wrote down mesh equations (that's just KVL for each loop in this case) and solved them for [itex]i_1[/itex] and [itex]i_2[/itex]. That's all you need to get [itex]V_1[/itex] and [itex]V_2[/itex].
     
  7. Apr 3, 2008 #6
    Ok, I see. Thanks for your help! I'll mark this as solved now.
     
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