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Capacitance (Potential Difference and Energy)

  1. Sep 30, 2015 #1
    1. The problem statement, all variables and given/known data
    In the figure C1 = 10.0 μF,C2 = 20.0 μF and C3 = 27.0 μF. If no capacitor can withstand a potential difference of more than 130 V without failure, what is (a) the magnitude of the maximum potential difference that can exist between points A and B and (b) the maximum energy that can be stored in the three-capacitor arrangement?
    http://edugen.wileyplus.com/edugen/courses/crs7165/art/qb/qu/c25/q37.jpg
    Image link - http://www.webassign.net/hrw8/25-45.gif
    2. Relevant equations
    1/Cseries= 1/C1 + 1/C2 ...
    U = q2/(2C) = (0.5)CV2

    3. The attempt at a solution
    For part A, I know that 130V goes into C1 and I think half that goes into C2 so 65V but I'm not sure how much goes into C3.
    For part B, I need the solution to part A to figure that out.

    Thank you!
     
  2. jcsd
  3. Sep 30, 2015 #2

    gneill

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    Staff: Mentor

    Can you justify that claim?
    Consider how charge is distributed amongst series-connected capacitors (when they are charged simultaneously by the same current).

    What relationship is there between voltage, charge, and capacitance?

    Edit: For part (b), consider a clever way to put as much energy as possible onto the arrangement.
     
  4. Sep 30, 2015 #3
    Actually I think I got part A. C = Q/V => V=Q/C the voltage for the first one is 130 so Q = (130)(10E-6) = 1.3E-3
    Then you use the Q value to find the rest? So C3 is 48.15?

    For part B, I just use the equation U = q2/(2C) = (0.5)CV2?
     
  5. Sep 30, 2015 #4

    gneill

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    Staff: Mentor

    That looks good.
    Yes,... but the question as posed does not restrict you to using the charges or voltages from part A...
     
  6. Sep 30, 2015 #5
    Do you just plug in each voltage with its respective capacitance to the equation and see which is higher or what is the other way?
     
  7. Sep 30, 2015 #6

    gneill

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    Staff: Mentor

    You want to maximize the total energy stored (while respecting the voltage tolerance of the individual components). So what would be the ideal situation?
     
  8. Oct 1, 2015 #7
    Only using the potential energy from the first capacitor?
     
  9. Oct 1, 2015 #8

    gneill

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    Staff: Mentor

    Wouldn't that be a waste of the energy storage potential of the other two?
     
  10. Oct 1, 2015 #9
    Add all of the potential energies together?
     
  11. Oct 1, 2015 #10

    gneill

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    Staff: Mentor

    Sure. After all, you have three "containers" and each can store some. Otherwise it's like having three boxes to put things in and only using the smallest one.
     
  12. Oct 1, 2015 #11
    Thank you i got it!
     
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