Conservation of charge, but not conservation of energyby imsickofweed Tags: charge, conservation, energy 

#1
Nov1909, 12:58 PM

P: 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 


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