Capacitor charged then Connected to another Capacitor.

In summary, when one capacitor with 4.0 J of stored energy is connected in parallel with an uncharged capacitor, the charge redistributes equally between the two capacitors and the electric field in each capacitor is cut in half. This leads to each capacitor now storing 1/4 of the original energy. The excess energy is lost due to the wire connection having some inductance and resistance, causing the energy to dissipate.
  • #1
Jonnyto
12
0

Homework Statement


One capacitor is charged until its stored energy is 4.0 J, the charging battery then being removed. A second uncharged capacitor is then connected to it in parallel. (a) If the charge distributes equally, what is now the total energy stored in the electric fields?(b) Where did the excess energy go?


Homework Equations


u=1/2*ε*E2 Where E is the electric field and u is the energy density(U/Volume)


The Attempt at a Solution


Okay so I'm somewhat lost. Since the charge is spread equally, and they are in parallel, so I assume they have the same capacitance. So for that I assumed that the total energy stored in each is half of that? However my reasoning is not correct since energy disappears? How can I approach the problem correctly?
 
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  • #2
Jonnyto said:

Homework Statement


One capacitor is charged until its stored energy is 4.0 J, the charging battery then being removed. A second uncharged capacitor is then connected to it in parallel. (a) If the charge distributes equally, what is now the total energy stored in the electric fields?(b) Where did the excess energy go?


Homework Equations


u=1/2*ε*E2 Where E is the electric field and u is the energy density(U/Volume)


The Attempt at a Solution


Okay so I'm somewhat lost. Since the charge is spread equally, and they are in parallel, so I assume they have the same capacitance. So for that I assumed that the total energy stored in each is half of that? However my reasoning is not correct since energy disappears? How can I approach the problem correctly?

The charge will redistribute between the two capacitors. Each of two capacitors will have half the charge of the original capacitor. How will that affect the electric field in each capacitor?
 
  • #3
Would that cut the electric field in half?
 
  • #4
Jonnyto said:
Would that cut the electric field in half?

Yes, it would. What will that do to the total stored energy?
 
  • #5
1/4 the original energy on each.
 
  • #6
Jonnyto said:
1/4 the original energy on each.

Right again. So now you've got half the energy you started with. Where did it go?
 
  • #7
Hmm that's what I'm unsure of now. Was this energy lost pushing the charge to the other capacitor?
 
  • #8
Jonnyto said:
Hmm that's what I'm unsure of now. Was this energy lost pushing the charge to the other capacitor?

Well, it has to flow through a wire. What kind of property of wire might make that not free?
 
  • #9
Jonnyto said:
Hmm that's what I'm unsure of now. Was this energy lost pushing the charge to the other capacitor?
Yes, but how exactly?
In the real world, the connection will have some inductance and some resistance, however small. What will that lead to?
 

Related to Capacitor charged then Connected to another Capacitor.

1. What is the purpose of connecting a charged capacitor to another capacitor?

Connecting a charged capacitor to another capacitor allows for the transfer of electrical energy between the two capacitors, resulting in a change in voltage or charge on each capacitor.

2. How does the voltage change when two capacitors are connected?

The voltage across each capacitor will be equalized when they are connected in parallel, meaning that the total voltage across both capacitors will remain the same, but the voltage on each capacitor will change.

3. Can the energy stored in a charged capacitor be transferred to another capacitor?

Yes, when a charged capacitor is connected to another capacitor, the energy stored in the first capacitor will be transferred to the second capacitor, resulting in a change in voltage or charge on both capacitors.

4. Will the capacitance of the two connected capacitors change?

No, the total capacitance of the two connected capacitors will remain the same. However, the capacitance of each individual capacitor may change depending on the material and geometry of the capacitors.

5. What happens to the charge on each capacitor after they are connected?

The charge on each capacitor will be redistributed after they are connected. The total charge on both capacitors will remain the same, but the charge on each individual capacitor may change depending on their initial voltages and capacitances.

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