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MHT CET202311 May 2023Morning ShiftPhysicsCapacitanceActual

Two identical capacitors have the same capacitance ' C '. One of them is charged to a potential V₁ and the other to V₂ . 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 ₁^2- V ₂^2 )
  2. B1 4 C (V₁^2+V₂^2 )
  3. C1 4 C (V₁-V₂ )^2
  4. D1 4 C ( V ₁+ V ₂ )^2

Correct answer

C. 1 4 C (V₁-V₂ )^2

Step-by-step solution

Initial energy of the combined system U ₁= 1 2 CV ₁^2+ 1 2 CV ₂^2= C 2 ( ~V ₁^2+ V ₂^2 ) On joining the two condensers in parallel, common potential, V = V ₁+ V ₂ 2 Final energy of the combined system: U ₂ 1 2 ( C + C ) ( V ₁+ V ₂ 2 )^2 . - Decrease in energy will be: aligned U & = U _ L - U ₂ & = C 2 ( ~V ₁^2+ V ₂^2 )- 1 2 ( C + C ) ( V ₁+ V ₂ 2 )^2 & = 1 4 C ( V ₁- V ₂ )^2 aligned

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