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

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

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G1 Physics · Accepted Answer

Total charge after connection: Q = CV + 2CV = 3CV Total capacitance: C(total) = 2C Common potential: V꜀ = Q/C(total) = 3CV/(2C) = 3V/2 Initial energy: Uᵢ = ½CV² + ½C(2V)² Final energy: U(final) = ½(2C)(3V/2)² Decrease in energy: ΔU = Uᵢ - U(final) = CV²/4