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Heat generated in the circuit

  1. May 15, 2014 #1
    1. The problem statement, all variables and given/known data

    How much heat is generated in the circuit after the switch is shifted from position 1 to 2?

    2. Relevant equations



    3. The attempt at a solution

    Let the charge on the right cap be Q(+Q on bottom plate) , on middle be Q-Q1(-Q+Q1 on bottom plate) and Q1(-Q1 on bottom plate) on left plate .

    Ceq = C(C+C0)/(2C+C0)

    Q=VC(C+C0)/(2C+C0)

    Q1=VC/(2C+C0)

    Q-Q1 = VCC0/(2C+C0)

    Now when the switch is at position1,charge on the bottom plate of left cap is -Q1 and after the switch is moved to position 2 charge is -Q i.e charge Q-Q1 has flown through the battery .In other words negative charge of magnitude Q-Q1 flows from positive to negative terminal of battery(current flows from negative to positive terminal) i.e work done by battery is (Q-Q1)V .

    Work done by battery = Change of energy stored in the capacitors + heat dissipated .

    So,heat dissipated = Work done by battery - Change of energy stored in the capacitors .

    Change of energy stored in the capacitors will be zero .

    Heat dissipated = Work done by battery = (Q-Q1)V = V2CC0/(2C+C0) .

    Is the answer correct ?

    Have I approached the problem correctly ?
     

    Attached Files:

    Last edited: May 15, 2014
  2. jcsd
  3. May 15, 2014 #2

    haruspex

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    That looks right to me.
     
  4. May 15, 2014 #3

    rude man

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    Yes. Any finite battery resistance will dissipate the same amount of energy. Interesting problem.
    (I did not check the delta stored energy).
     
  5. May 15, 2014 #4
    Thanks haruspex and rude man .

    Do you agree that if the switch were initially at position 2 and moved from position 2 to 1 then in that case also the result obtained in the OP would remain same ?
     
  6. May 15, 2014 #5
    I haven't checked all the math but the approach seems correct. The equation you provided for Q1 is missing something. The units don't match.
     
  7. May 15, 2014 #6

    haruspex

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    Yes, it's symmetric.
     
  8. May 16, 2014 #7
    Thanks everyone for your valuable inputs .
     
  9. May 16, 2014 #8

    NascentOxygen

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