12 December 2014 11 1K Report

This is a well known old problem:

When a charged capacitor is connected to an uncharged capacitor, they share their charges, but there is an energy loss during this process; even when there is no resistor in the circuit.

Let's assume two identical capacitors (C1=C2=C); one charged (Q1=Q, V1=Q/C=V) and the other empty (Q2=0, V2=0).

Then, when they are connected in parallel via ideal conductors, charge sharing occurs and finally they exhibit Q1=Q2=Q/2, V1=V2=(Q/C)/2=V/2.

The initial energy in the system was, Ei=CV2/2 (the energy stored on C1 only; because C2 had zero charge / zero energy initially).

After charge sharing, the final energy is, Ef=C(V/2)2/2+C(V/2)2/2=CV2/4

In the above example, Ef=Ei/2; i.e. half of the energy is lost.

"How? In what form? Or, is there anything Circuit Theory is missing?"

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P.S.: Honestly speaking, I do have some ideas (though limitied) about the answer, for I have heard or read some explanations on several occasions (Some explanations were made in books and scientific magazines as well), nevertheless I wanted to see what other alternative concise explanations we (researchers in ResearchGate) can propose.

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