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BITSAT2013PhysicsCapacitanceActual

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 the positive ends are also connected, the decrease in energy of the combined system is -

Options

  1. A1 4 C ( V ₁²- V ₂² )
  2. B1 4 C (V₁²+V₂² )
  3. C1 4 C ( V ₁- V ₂ )²
  4. D1 4 C (V₁+V₂ )²

Correct answer

C. 1 4 C ( V ₁- V ₂ )²

Step-by-step solution

Initial energy of combined system U ₁= 1 2 CV ₁²+ 1 2 CV ₂² Final common potential, V = V ₁+ V ₂ 2 , Final energy of system, U ₂=2 1 2 C ( V ₁+ V ₂ 2 )² Hence loss of energy = U ₁- U ₂ = 1 4 C ( V ₁- V ₂ )²

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