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MHT CET202527 Apr 2025Evening ShiftPhysicsCapacitanceActual

Air capacitor has capacitance of 1 ~F . Now the space between two plates of capacitor is filled with two dielectrics as shown in figure. The capacitance of the capacitor is ( d = distance between two plates, K ₁ and K ₂ are dielectric constants of two dielectrics respectively)

Options

  1. A12 ~F
  2. B6 ~F
  3. C8 3 ~F
  4. D3 ~F

Correct answer

A. 12 ~F

Step-by-step solution

The air capacitance C₀ = ₀ A d = 1 F establishes the base relationship between plate area and separation. With two dielectrics dividing the plate area equally, the system forms two parallel capacitors. For dielectric K₁ = 8 occupying half the area: C₁ = K₁ ₀ (A/2) d = 4 ₀ A d = 4C₀ Similarly, for dielectric K₂ = 4 : C₂ = K₂ ₀ (A/2) d = 2 ₀ A d = 2C₀ The parallel combination yields: C_ eq = C₁ + C₂ = 4C₀ + 2C₀ = 6C₀ = 6 F Final answer: 6 F

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