What Happens to Charge and Energy When Connecting Capacitors in Parallel?

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When connecting an uncharged capacitor in parallel with a fully charged capacitor of equal capacitance, the charge distribution changes due to the conservation of charge and energy principles. The initial energy stored in the charged capacitor is equal to the energy after connection, but energy losses occur, resulting in less total energy in the system. The final voltage across both capacitors is Vf = Vi/sqrt(2), leading to a total charge Qt that appears to contradict the initial charge. While charge is conserved, energy is not, as some energy is dissipated as heat during the process. This highlights the distinction between charge conservation and energy conservation in capacitor circuits.
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I am not sure if I have full understanding of capacitors energy, because I found a contradiction in solving one problem. The problem is: -
If an uncharged capacitor connected to another fully charged capacitor in parallel, what will be the new charge distribution on both capacitors? “Assuming equal capacitance”
I believe we have two rules of respect:-
1- Conservation of charge
2- Conservation of energy
If we assume that C = capacitance, and Vi = initial voltage and Qi=the initial charge on the charged capacitance.
Let the energy before connecting the two capacitance equal to the energy after linking them together:-

0.5*C*Vi^2 = 0.5*(2C)*Vf^2
then: - Vf=Vi/sqrt(2)

Know consider the total charge after linking both capacitors:-

Qt = Ct * Vf= (2C)*Vi/sqrt(2)=C*Vi*sqrt(2)

Which is obviously not equal to C*Vi “the initial charge”.

I am confused which one of these two fundamental concepts I have to base my calculation in, and why it doesn’t work with the other concept.
 
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