Find the equivalent capacitance for the capacitor arrangement shown in the original question figure. The three dielectric constants are K₁, K₂ and K₃; plate area is A and separation is d.
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Question

Find the equivalent capacitance for the capacitor arrangement shown in the original question figure. The three dielectric constants are K₁, K₂ and K₃; plate area is A and separation is d.

G1 Physics · Accepted Answer

From the geometry in the original figure, C₁ = Aε₀K₁/d, C₂ = Aε₀K₂/d, C₃ = Aε₀K₃/(2d). C₁ and C₂ are in series: C₁′ = Aε₀K₁K₂/[d(K₁+K₂)]. This is in parallel with C₃: C e q C_eq C e ​ q = C₁′ + C₃ = (Aε₀/d) [(2K₁K₂+K₂K₃+K₃K₁)/(2(K₁+K₂))].