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MHT CET 2021 (24 Sep, Shift 1) · Charge Sharing & Loss of Energy

Charge Sharing & Loss of Energy question from MHT CET 2021 (24 Sep, Shift 1)

Q24MHT CET 2021 · 24 SEP · SHIFT 1Medium

Charge Sharing & Loss of Energy

Two identical capacitors have the same capacitance ' $C$ '. One of them is charged to potential ' $V_1$ ' and the other to $V_2$ . The negative ends of the capacitors are connected together. When positive ends are also connected, the decrease in energy of the combined system is

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Answer: (a)

Loss on joining like plates: $\Delta U = \frac{1}{2}\frac{C_1C_2}{C_1 + C_2}(V_1 - V_2)^2$
With equal $C$ : $\frac{C_1C_2}{C_1 + C_2} = \frac{C}{2}$
$\Delta U = \frac{1}{4}C(V_1 - V_2)^2$ , so the answer is (a).

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