A parallel plate capacitor with plate area A and separation d has an initial capacitance C₀ when there is air between the plates. It is then filled with three different dielectric materials. The left half of the space (thickness d/2 , full area A ) is filled with a dielectric of constant K₁ = 2 . The right half of the space (thickness d/2 ) is divided into two equal parts, each of area A/2 , and filled with dielectri

Step-by-step solution

The initial capacitance with air is C₀ = ₀ A d . The system can be modeled as a capacitor C₁ in series with the parallel combination of capacitors C₂ and C₃ . For the left half (thickness d/2 , area A ): C₁ = K₁ ₀ A d/2 = 2K₁ ( ₀ A d ) = 2(2)C₀ = 4C₀ . For the right half, it is split into two equal areas ( A/2 ) with thickness d/2 : C₂ = K₂ ₀ (A/2) d/2 = K₂ ( ₀ A d ) = 3C₀ . C₃ = K₃ ₀ (A/2) d/2 = K₃ ( ₀ A d ) = 5C₀ . C₂ and C₃ are in parallel, so their equivalent capacitance is: C_p = C₂ + C₃ = 3C₀ + 5C₀ = 8C₀ . No