pat666 said:
Hey kuruman, just one more question if you have time or see this.. with the explanation - I don't understand where the energy could have gone? How can energy not be conserved in a closed system?
Not all closed systems necessarily conserve mechanical energy which is what we are talking about here. Consider the totally inelastic collision where mass m
1 is moving with initial speed v
0 and collides with m
2 initially at rest. The two masses move together after the collision and their common speed is the speed of the center of mass, namely
V=\frac{m_1v_0}{m_1+m_2}
If you calculate the final energy of the "closed" system, you get (after a bit of algebra)
K_f=\frac{1}{2}m_1v^{2}_{0} \left( \frac{m_1}{m_1+m_2} \right)
This is clearly less than the initial energy
K_i=\frac{1}{2}m_1v^{2}_{0}
Where did the energy go? The stock answer is "Heat generated by friction."
This capacitor problem is exactly analogous to the totally inelastic collision. The symbols are different but the math is the same. Here is why
Momentum (p) is conserved becomes charge (q) is conserved.
Definition p = mv is replaced by definition q = CV, i.e. capacitance (C) is the analogue of mass (m) and voltage (V) is the analogue of velocity (v).
Kinetic energy=(1/2)mv
2 becomes Energy stored=(1/2)CV
2.
So the prediction is that the energy remaining in the system is the analogue of K
f, namely
E_f=\frac{1}{2}C_1V^{2}_{0} \left( \frac{C_1}{C_1+C_2} \right)
Put in the numbers and see what you get.
As for "where did the energy go?", complete the analogy. If heat production by friction accounts for loss of mechanical energy in a collision, what accounts for loss of mechanical energy in a circuit and how is it generated?
