Change in total energy of capacitance

[roxanne.w]

Homework Statement

When an initially charged capacitor is connected in a circuit with an uncharged capacitor, why would the total energy of both capacitors be less than the initial energy of the charged capacitor?

Homework Equations

This was a question asking for an explanation, so I'm not sure if any equations are relevant here.
1/C = 1/C₁ + 1/C₂

The Attempt at a Solution

Would it be due to heat dissipated in the circuit when the charge (or current?) flows in the circuit? Also, the suggested explanation was that a spark was produced - why and where this happens, I don't really know.

Thanks for your help!

 

[NascentOxygen]

Hi roxanne.w, welcome to PF.

You have used conservation of charge to prove that the total energy after they are connected is less? Yes, the explanation is that energy is lost in resistance, that of the wire and of the foil comprising the capacitor. Energy from the spark radiates into space as light and other EM radiation.

 

[rude man]

Homework Statement

When an initially charged capacitor is connected in a circuit with an uncharged capacitor, why would the total energy of both capacitors be less than the initial energy of the charged capacitor?

Homework Equations

This was a question asking for an explanation, so I'm not sure if any equations are relevant here.
1/C = 1/C₁ + 1/C₂

The Attempt at a Solution

Would it be due to heat dissipated in the circuit when the charge (or current?) flows in the circuit? Also, the suggested explanation was that a spark was produced - why and where this happens, I don't really know.

Thanks for your help!

You have assumed Kirchhoff's laws in determining before-and-after energies. Therefore, radiation is excluded as a mechanism for explaining energy loss.

The correct answer is heat dissipation or, if we assume zero resistance, which is theoretically possible in a cryogenic environment, finite inductance resulting in non-decaying current oscillations, with the charges moving back and forth between capacitors. In this latter case there is indeed conservation of energy, the sum of capacitive and inductive energies at any instant being constant = 1/2 Cv²(0+) if we assume one capacitor C had all the original charge Q = Cv(0+).
.