A parallel plate capacitor of capacitance ' C ' is connected to a… | MHT CET 2024 (9 May, Shift 1)

Q12MHT CET 2024 · 9 MAY · SHIFT 1Medium

Charge Sharing & Loss of Energy

A parallel plate capacitor of capacitance ' $C$ ' is connected to a battery and charged to a potential difference ' $V$ '. Another capacitor of capacitance 3 C is similarly charged to a potential difference 3 V. The charging battery is then disconnected and capacitors are connected in parallel to each other in such a way that positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is

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Answer: (b)

Charges $CV$ and $3C \times 3V = 9CV$ ; opposite plates joined, net charge $= 8CV$ .
Common potential $V' = \frac{8CV}{4C} = 2V$
$U = \frac{1}{2}(4C)(2V)^2 = 8CV^2$
So the answer is (b).

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