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A parallel plate capacitor has a capacitance C₀ when there is air between its plates, which are separated by a distance d . Two dielectric slabs are inserted between the plates, parallel to them. The first slab has a thickness of d 2 and a dielectric constant of 4 . The second slab has a thickness of d 4 and an unknown dielectric constant K . The remaining space between the plates is filled with air. If the new equiv

Options

  1. A8
  2. B4
  3. C2
  4. D0.5

Correct answer

C. 2

Step-by-step solution

Initial capacitance is C₀ = ₀ A d . When dielectric slabs are inserted, the equivalent capacitance is given by C = ₀ A t₁ K₁ + t₂ K₂ + t₃ K₃ . The thicknesses of the regions are t₁ = d 2 , t₂ = d 4 , and the remaining air space is t₃ = d - ( d 2 + d 4 ) = d 4 . Substituting the given values: C = ₀ A d/2 4 + d/4 K + d/4 1 C = ₀ A d ( 1 8 + 1 4K + 1 4 ) C = C₀ 3 8 + 1 4K Given that C = 2C₀ , we have: 2C₀ = C₀ 3 8 + 1 4K 3 8 + 1 4K = 1 2 1 4K = 1 2 - 3 8 = 1 8 4K = 8 K = 2 Answer: 2

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