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Capacitance Circuit

  1. Dec 30, 2012 #1
    1. The problem statement, all variables and given/known data

    5kivma.png

    Initial Conditions
    (a)
    Switch S2 kept open, switch S1 closed until C1, C2 and C3 are fully charged. What is the potential difference across each capacitor? Now Switch S2 is closed. What is the new potential difference across each capacitor?

    (b) Switches S1 and S2 are both closed. What is the p.d. across each capacitor?


    3. The attempt at a solution

    (a)
    Before S2 is closed, p.d. across all 3 capacitors are the same:

    V1 = V2 = V3 = 80V
    V4 = 0V

    After S2 is closed, capacitors 2 and 3 do not affect the circuit at all hence they retain the p.d. of 80V.

    C1 distributes half of its charge to C4.

    V2 = V3 = 80V

    C1 = C4 = 40V


    (b)

    C1 and C4 are in parallel, so C1,4 = 2C

    thus it is C1,4, C2 and C3 in series. Hence p.d. across each is:

    V2 = V3 = 96V
    V1,4 = V1 = V4 = 48V
     
  2. jcsd
  3. Dec 30, 2012 #2

    mfb

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    Looks correct. You could add the formula you used at (b).
     
  4. Dec 31, 2012 #3
    Thanks!
     
  5. Jan 3, 2013 #4
    Do all capacitors have the same capacitance?

    If yes, then your answer is correct. If not, you must use the conservation of charge to calculate the potential difference for each capacitor.

    J.
     
  6. Jan 3, 2013 #5

    SammyS

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    By the way, this thread should be in the Introductory Physics section.

    I'm assuming that initially, before either switch is closed all the capacitors are discharged.

    Then S1 is closed & S2 is open, with C1, C2 and C3 becoming fully charged.
    At this point, each of the three capacitors is charged equally. If they all have the same capacitance, then they will each have the same p.d., as in your analysis.​
    Then for part (a), S1 is opened followed by S2 being closed.
    If capacitors, C1 & C4, have the same capacitance, then they will be charged equally.

    If not, then you can use the fact that they will have the same p.d. to find the charge on each, keeping in mind to employ conservation of charge.​

    For part (b): (Your answer is incorrect even if all the capacitances are equal.)

    What is the equivalent capacitance of the 4 capacitors?
     
    Last edited: Jan 3, 2013
  7. Jan 3, 2013 #6

    berkeman

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    Moved to Intro Physics.
     
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