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MHT CET202123 Sep 2021Morning ShiftPhysicsCapacitanceActual

Two identical capacitors have the same capacitance ' C '. One of them is charged to potential ' V₁ ' and the other to V₂ . The negative ends of the capacitors are connected together. When positive ends are also connected, the decrease in energy of the combined system is

Options

  1. A1 4 C ( V ₁- V ₂ )^2
  2. B1 2 C ( V ₁^2+ V ₂^2 )
  3. C1 2 C ( V ₁^2- V ₂^2 )
  4. D1 2 C ( V ₁+ V ₂ )^2

Correct answer

A. 1 4 C ( V ₁- V ₂ )^2

Step-by-step solution

Q ₁= CV ₁, Q ₂= CV ₂, Q = Q ₁+ Q ₂=2 CV After connection, aligned & CV ₁+ CV ₂=2 CV & V = V ₁+ V ₂ 2 aligned Decrease in energy = 1 2 CV ₁^2+ 1 2 CV ₂^2- 1 2 (2 C ) ( V ₁+ V ₂ 2 )^2 = 1 4 C ( V ₁- V ₂ )^2

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