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MHT CET20244 May 2024Morning ShiftPhysicsCapacitanceActual

A parallel plate air capacitor, with plate separation ' d ' has a capacitance of 9 pF . The space between the plates is now filled with two dielectrics, the first having K ₁=3 and thickness d ₁= d / 3 , while the 2^ nd has K ₂=6 and thickness d ₂=2 ~d / 3 . The capacitance of the new capacitor is

Options

  1. A3.8 pF
  2. B20.25 pF
  3. C40.5 pF
  4. D45 pF

Correct answer

C. 40.5 pF

Step-by-step solution

For a parallel plate capacitor, with dielectric C = A ₀ k ~d ...(i) C₁= A ₀ k₁ d₁ = A ₀ 3 d / 3 =9 A ₀ d =9 C [ From (i) ]C₂= A ₀ k₂ d₂ = A ₀ 6 2 d / 3 =9 A ₀ d =9 C [ From (i) ] As they both are in series, C _ total = C ₁ C ₂ C ₁+ C ₂ = 9 C 9 C 9 C +9 C = 9 2 C = 9 2 9 10⁻¹² C _ total =40.5 pF

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