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Two Capacitor problem

  1. May 14, 2014 #1
    1. The problem statement, all variables and given/known data

    Two capacitors ##C_1## and ##C_2## (where ##C_1 > C_2##) are charged to the same initial potential difference ##V_i##, but with opposite polarity. The charged capacitors are removed from the battery, and their plates are connected as shown in Figure a. The switches ##S_1## and ##S_2## are then closed, as shown in Figure b. Find the final potential difference ##V_f## between a and b after the switches are closed


    2. Relevant equations



    3. The attempt at a solution

    Let Vf be final potential difference.

    ## V_f = \frac{Q_{1f}}{C_1} = \frac{Q_{2f}}{C_2}##
    ## Q_1-Q_2 = Q_{1f}+Q_{2f}##
    ## Q_1-Q_2 = Q_{1f}+\frac{C_2}{C_1}Q_{1f}##
    ## C_1V_i-C_2V_i = \frac{C_1+C_2}{C_1}Q_{1f}##

    ## V_f = \frac{C_1-C_2}{C_1+C_2}V_i##

    Is this correct ?
     

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  2. jcsd
  3. May 15, 2014 #2

    ehild

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    Gold Member

    Yes.

    ehild
     
  4. May 16, 2014 #3
    Many thanks ehild :)
     
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