Three parallel plate capacitors each with area A and separation d are filled with two dielectrics ( k₁ and k₂) in the following fashion. Which of the following is true? (k₁ > k₂) (a) CC > CB > CA (b) CB > CC > CA (c) CA > CC > CB (d) CC > CA > CB

Answer: (c). Take C₀=(ε₀A)/(d), k₁=2, k₂=1 to compare. A: top k₁ layer ( 2k₁C₀) in series with bottom pair in parallel ( (k₁+k₂)C₀): CA=(2k₁(k₁+k₂))/(3k₁+k₂)C₀=12/7C₀ B: same with k₂ on top: CB=(2k₂(k₁+k₂))/(3k₂+k₁)C₀=6/5C₀ C: two columns, each k₁,k₂ in series: CC=(2k₁k₂)/(k₁+k₂)C₀=4/3C₀ 1.71>1.33>1.2, so the answer is (c) CA>CC>CB.

Three parallel plate capacitors each with area A and separation d are… | JEE Main 2026 (24 Jan, Shift 2)

Q20JEE Main 2026 · 24 JAN · SHIFT 2Medium

Dielectrics

Three parallel plate capacitors each with area $A$ and separation $d$ are filled with two dielectrics ( $k_1$ and $k_2$ ) in the following fashion. Which of the following is true?

$(k_1 > k_2)$

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Answer: (c)

Take $C_0=\frac{\epsilon_0A}{d}$ , $k_1=2$ , $k_2=1$ to compare.
A: top $k_1$ layer ( $2k_1C_0$ ) in series with bottom pair in parallel ( $(k_1+k_2)C_0$ ): $C_A=\frac{2k_1(k_1+k_2)}{3k_1+k_2}C_0=\frac{12}{7}C_0$
B: same with $k_2$ on top: $C_B=\frac{2k_2(k_1+k_2)}{3k_2+k_1}C_0=\frac{6}{5}C_0$
C: two columns, each $k_1,k_2$ in series: $C_C=\frac{2k_1k_2}{k_1+k_2}C_0=\frac{4}{3}C_0$
$1.71>1.33>1.2$ , so the answer is (c) $C_A>C_C>C_B$ .

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