Three parallel plate capacitors each with area A and separation d are filled with two dielectric (k₁ and k₂) in the following fashion. Which of the following is true? (k₁ > k₂)

Question

G1 Physics · Accepted Answer

Let C₀ = ε₀A/d. Each half-area, half-thickness dielectric block has capacitance Kε₀(A/2)/(d/2) = KC₀. For arrangement A: One parallel branch contains two k₁C₀ capacitors in series: C(A,1) = k₁C₀/2. The other branch contains k₁C₀ and k₂C₀ in series: C(A,2) = k₁k₂C₀/(k₁+k₂). Therefore, C(A) = k₁C₀/2 + k₁k₂C₀/(k₁+k₂) = k₁C₀(k₁+3k₂)/ [2(k₁+k₂)]. For arrangement B: One branch contains two k₂C₀ capacitors in series: C(B,1) = k₂C₀/2. The other branch again contains k₁C₀ and k₂C₀ in series. Hence, C(B)…

Three parallel plate capacitors each with area A and separation d are filled with two dielectric (k₁ and k₂) in the following fashion. Which of the following is true? (k₁ &gt; k₂)

Three parallel plate capacitors each with area A and separation d are filled with two dielectric (k₁ and k₂) in the following fashion. Which of the following is true? (k₁ > k₂)