Conservation of charge, but not conservation of energy

[imsickofweed]

Homework Statement

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

Homework 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)

The Attempt at a Solution

I'm just not sure how to set up the equations to show that it works.

 

[Valkarie]

I know that the total charge is conserved, but I'm not sure how to show it mathematically. Can someone point me in the right direction?

 

[Mene]

it is important to understand the concept of conservation of charge and conservation of energy. Conservation of charge states that the total charge in a closed system remains constant, while conservation of energy states that energy cannot be created or destroyed, only transferred or transformed from one form to another.

In this scenario, we can see that the total charge in the system remains constant. At t=0, the charge on C1 is not equal to 0, but when the switch is closed, the charge on C2 becomes 0, balancing out the total charge in the system. This shows that conservation of charge is indeed present in this system.

However, we can also see that there is a loss of energy in the system. As the capacitors charge up, there is a flow of current through the resistor, which results in heat being dissipated. This energy loss is shown in the equations provided, where the energy lost is equal to the power (I^2R) multiplied by the time over which it is lost. This shows that conservation of energy is not present in this system.

In conclusion, while conservation of charge is present in this system, conservation of energy is not. This highlights the importance of understanding both concepts in order to fully understand the behavior of a system.