Conservation of charge, but not conservation of energy

  1. 1. The problem statement, all variables and given/known data

    A DC voltage (V) in series with a resistor of value R and in series with a capacitor (C1) at time t=0 a switch closes to put another capacitor (C2) in parallel with C1 and in series with V and R. The charge on C1 at t=0- Q1(0-)=/0 (doesn't equal 0) and charge on C2 at t=0- Q2(0-)=0 at time t=0+ C2 begins to charge and eventually comes to equilibrium. Show conservation of charge exists and that conservation of energy doesn't exist

    2. Relevant equations

    energy lost = power x time = ∫I(t)2 R dt

    I(t) = \frac{V_1\,-\,V_0}{R}\,e^{-\frac{1}{CR}\,t}

    V_1\ -\ V(t) = (V_1\,-\,V_0)\,e^{-\frac{1}{CR}\,t}

    Energy lost (to heat in the resistor):

    \int\,I^2(t)\,R\,dt\ =\ \frac{1}{2}\,C (V_1\,-\,V_0)^2[/itex]

    Efficiency (energy lost per total energy):

    [tex]\frac{V_1^2\,-\,V_0^2}{V_1^2\,-\,V_0^2\,+\,(V_1\,-\,V_0)^2}\ =\ \frac{1}{2}\,\left(1\,+\,\frac{V_0}{V_1}\right)


    3. The attempt at a solution

    I'm just not sure how to set up the equations to show that it works.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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