A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with three dielectric materials with constants k₁, k₂ and k₃ in regions shown. If a single dielectric material is used instead to give the same capacitance, the dielectric constant is given by: [Diagram: Image]
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Question

A parallel-plate capacitor of area A, plate separation d and capacitance C is filled with three dielectric materials with constants k₁, k₂ and k₃ in regions shown. If a single dielectric material is used instead to give the same capacitance, the dielectric constant is given by: [Diagram: Image]

Options

G1 Physics · Accepted Answer

Step 1: Divide the capacitor cross-section into three parallel-strip regions as shown in the source diagram. Step 2: For each strip compute capacitance Cᵢ = ε₀kᵢAᵢ/dᵢ and account for the series dielectric layers. Step 3: Add the parallel branch capacitances to get C(eq); compare with ε₀K(eff) A/d. Step 4: Source marks option (C).