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Potential in capacitance network

  1. Sep 23, 2009 #1
    1. The problem statement, all variables and given/known data

    A capacitance matrix represents the charge coupling within a group of conductors — that is, the relationship between charges and voltages for the conductors. Given the three conductors shown in the following link, with the outside boundary taken as a reference,

    http://i1021.photobucket.com/albums/af335/hectoryx/capacitancenetwork.jpg


    2. Relevant equations

    the net charge on each object will be:

    [tex]$\begin{array}{l}
    {Q_1} = {C_{10}}{V_1} + {C_{12}}({V_1} - {V_2}) + {C_{13}}({V_1} - {V_3}) \\
    {Q_2} = {C_{20}}{V_2} + {C_{12}}({V_2} - {V_1}) + {C_{23}}({V_2} - {V_3}) \\
    {Q_3} = {C_{30}}{V_3} + {C_{13}}({V_3} - {V_1}) + {C_{23}}({V_3} - {V_2}) \\
    \end{array}$
    [/tex]


    3. The attempt at a solution


    The problem is, if all of the capacitances are already known, and [tex] {V_1} - {V_2} = U [/tex] is also known, but [tex]{V_1}[/tex] and [tex]{V_2}[/tex] is not known.

    then how to calculate [tex]{V_3} [/tex] or [tex]{Q_3}[/tex]?

    Thanks in advance.

    Regards

    Hector
     
  2. jcsd
  3. Sep 24, 2009 #2

    turin

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    Homework Helper

    I don't believe that it is possible. You have six unknowns, but only four equations. Do you know any other values besides just V1-V2? Two more independent values should do it.
     
  4. Sep 25, 2009 #3
    Thanks for your reply.

    However, in the equivalent circuit of the capacitor network, the voltage of conductor 3 to the reference ground can be caculated.......so...
     
  5. Sep 25, 2009 #4

    turin

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    Homework Helper

    Are you suggesting that this is possible if you only know V1-V2? I don't believe so. If you simply mean that, yes, there is this additional input information, then the solution is trivial: V3=V3, right? I must not be understanding your problem.
     
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