Two identical capacitors have the same capacitance C. One of them is charged to a potential V and the other to a potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is

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(4) 1/4CV². Initial energy: Uᵢ=1/2CV²+1/2C(2V)²=1/2CV²+2CV²=5/2CV². Like plates are joined, so the total charge CV+2CV=3CV is shared by a total capacitance 2C: common voltage V_f=(3CV)/(2C)=(3V)/2. Final energy: U_f=1/2(2C)((3V)/2)²=C·(9V²)/4=9/4CV². Decrease =(10)/4CV²-9/4CV²=1/4CV², lost as heat in the connecting wires.

Two identical capacitors have the same capacitance C. One of them is charged to a potential V and the other to a potential 2V. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is

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