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COMEDK2025PhysicsCapacitanceActual

In the given figure all the capacitors ( C ₁, C ₂, C ₃ ) and ( C ₄ ) have the same capacitance (4 F ). The emf of the cell is 12 V. What is the effective capacitance ?

Options

  1. A(C_ eff =10 ~F )
  2. B(C_ eff =1 ~F )
  3. C(C_ eff =16 ~F )
  4. D(C_ eff =12 ~F )

Correct answer

A. (C_ eff =10 ~F )

Step-by-step solution

The circuit consists of three parallel branches connected across the 12 V source. Let the left node be A and the right node be B. Branch 1 consists of capacitors C₁ and C₂ in series. Their equivalent capacitance C₁₂ is given by 1 C₁₂ = 1 C₁ + 1 C₂ = 1 4 + 1 4 = 2 4 = 1 2 . Thus, C₁₂ = 2 F . Branch 2 consists of capacitor C₃ . Thus, C_ branch2 = C₃ = 4 F . Branch 3 consists of capacitor C₄ . Thus, C_ branch3 = C₄ = 4 F . Since these three branches are connected in parallel between nodes A and B, the effective capaci

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