MHT CET202410 May 2024Morning ShiftPhysicsCapacitanceActual
Two identical capacitors have the same capacitance ' C '. One of them is charged to potential V ₁ and other to V ₂ . The negative ends of capacitors are connected together. When positive ends are also connected, the decrease in energy of the combined system is
Options
- A1 4 C ( V ₁^2+ V ₂^2 )
- B1 4 C ( V ₁^2- V ₂^2 )
- C1 4 C (V₁+V₂ )^2
- D1 4 C ( V ₁- V ₂ )^2
Correct answer
D. 1 4 C ( V ₁- V ₂ )^2
Step-by-step solution
U _ i = 1 2 CV ₁^2+ 1 2 C V₂^2= 1 2 C ( ~V ₁^2+ V ₂^2 ) When the capacitors are joined, common potential, V = CV ₁+ CV ₂ 2 C = V ₁+ V ₂ 2 Final energy of the system, aligned U _ f & = 1 2 (2 C ) V ^2= 1 2 2 C ( ~V ₁+ V ₂ 2 )^2 & = 1 4 C ( ~V ₁+ V ₂ )^2 aligned aligned Decrease in energy & = U _ i - U _ f & = 1 4 C ( ~V ₁- V ₂ )^2 aligned