When two identical capacitors are charged individually to different potentials and connected parallel to each other, after disconnecting them from the source :

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net charge on connected plates equals the sum of initial charges.

the net potential difference across them is different from the sum of the individual initial potential differences.

net charge on connected plates is less than the sum of initial individual charges.

the net energy stored in the two capacitors is less than the sum of the initial individual energies.

answer is B, C, D.

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Detailed Solution

Apply KVL in the loop

$\frac{- Q_{2} - q}{C} + \frac{Q_{1} - q}{C} = 0 q = \frac{Q_{1} + Q_{2}}{2}$

So the final charges on both the capacitors will be $Q_{1}' = Q_{2}' = \frac{Q_{1} + Q_{2}}{2}$

So the net charge on connected plates equals the sum of initial charges.

And the capacitors will have a common potential of $V_{C M} = \frac{Q_{1} + Q_{2}}{2 C} = \frac{1}{C} x \frac{C V_{1} + C V_{2}}{2} = \frac{V_{1} + V_{2}}{2}$

$U_{i} = \frac{1}{2} {CV}_{1}^{2} + \frac{1}{2} {CV}_{2}^{2} U_{f} = \frac{1}{2} (2 C) {(V_{CM})}^{2} = \frac{1}{2} 2 C {(\frac{V_{1} + V_{2}}{2})}^{2} = C {(\frac{V_{1} + V_{2}}{2})}^{2}$

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