Charge relocation for Parallel Capacitors

[TRovang]

The question states: A charged capacitor C has stored energy U = 10.0J. A second, equal but initially uncharged capacitor (no energy stored) is then connected to the first in parallel.
(a) What is the new net energy stored after the charge is redistributed?
(b) Where did the excess energy go?Relevant equations include:
U = 1/2*Q²/C
V = Q/C

The Attempt at a Solution

My attempt is stating that the voltage drop across both capacitors will be the same once the second is placed in parallel. This gives me the equation:
V = Q_o/C_o = Q₁/C₁

Also, since the capacitance adds together I get C₁ = 2*C_o

Thus, using the first equation and the second I got Q_o = 1/2*Q₁

Now I have U = 10.0 = Q_o²/(2*C_o)

However the denominator is simply C₁ so I get C₁*10.0 = Q_o²

Now subbing in for Q_o I finally get C₁*10.0 = Q₁²/4.

This rearranges to give 20 = Q₁²/(2*C₁) = U₁.

Thus I find that the new net energy stored is actually 20J. This implies that part (b) makes absolutely no sense or I am completely wrong in my derivations.

Any help would be greatly appreciated.

 

[berkeman]

The question states: A charged capacitor C has stored energy U = 10.0J. A second, equal but initially uncharged capacitor (no energy stored) is then connected to the first in parallel.
(a) What is the new net energy stored after the charge is redistributed?
(b) Where did the excess energy go?


Relevant equations include:
U = 1/2*Q²/C
V = Q/C

The Attempt at a Solution

My attempt is stating that the voltage drop across both capacitors will be the same once the second is placed in parallel. This gives me the equation:
V = Q_o/C_o = Q₁/C₁

Also, since the capacitance adds together I get C₁ = 2*C_o

Thus, using the first equation and the second I got Q_o = 1/2*Q₁

Now I have U = 10.0 = Q_o²/(2*C_o)

However the denominator is simply C₁ so I get C₁*10.0 = Q_o²

Now subbing in for Q_o I finally get C₁*10.0 = Q₁²/4.

This rearranges to give 20 = Q₁²/(2*C₁) = U₁.

Thus I find that the new net energy stored is actually 20J. This implies that part (b) makes absolutely no sense or I am completely wrong in my derivations.

Any help would be greatly appreciated.

It looks like your initial assumptions are not right.

Start with the one capacitor all by itself, and Qo = Co * Vo

After you connect the 2nd capacitor, the charge Q gets evenly distributed across the two capacitors, so the voltage drops. What does it drop to? What is the initial energy of the one cap at the higher voltage compared to the final energy of the two caps at the lower voltage?

Then for part b -- this is a very commonly asked question for this problem. You can probably find it with a search here at the PF (it gets asked quite often), but basically the way to get a handle on it is to put a test resistor between the two caps, and work out the energy loss in the resistor as you connect the two caps together. Do this with a value R, and then a value R/10, and a value R/100, and so on. Do you see something useful ?