Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Conservation of charge, but not conservation of energy

  1. Nov 19, 2009 #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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted
Similar Discussions: Conservation of charge, but not conservation of energy
Loading...