Physics · Capacitors and R-C Circuits

JEE Main 2026 — 24 January, Evening Shift — Question 35

Three parallel plate capacitors each with area A and separation d are filled with two dielectric ( k1\mathrm{k}_{1} and k2\mathrm{k}_{2} ) in the following fashion. Which of the following is true? (k1>k2)\left(\mathrm{k}_{1}>\mathrm{k}_{2}\right)

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  1. Option A:

    CB>CC>CA\mathrm{C}_{\mathrm{B}}>\mathrm{C}_{\mathrm{C}}>\mathrm{C}_{\mathrm{A}}

  2. Option B:

    CC>CB>CA\mathrm{C}_{\mathrm{C}}>\mathrm{C}_{\mathrm{B}}>\mathrm{C}_{\mathrm{A}}

  3. Option C:

    CC>CA>CBC_{C}>C_{A}>C_{B}

  4. Option D:

    CA>CC>CB\mathrm{C}_{\mathrm{A}}>\mathrm{C}_{\mathrm{C}}>\mathrm{C}_{\mathrm{B}}

    Correct

Answer: D

Step-by-step solution

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For CA\mathrm{C}_{\mathrm{A}} : Let ε0 A d=C\frac{\varepsilon_{0} \mathrm{~A}}{\mathrm{~d}}=\mathrm{C} ∴CA=K1C2+K1 K2CK1+K2\therefore \mathrm{C}_{\mathrm{A}}=\frac{\mathrm{K}_{1} \mathrm{C}}{2}+\frac{\mathrm{K}_{1} \mathrm{~K}_{2} \mathrm{C}}{\mathrm{K}_{1}+\mathrm{K}_{2}} =K1C[K1+2 K22( K1+K2)]=\mathrm{K}_{1} \mathrm{C}\left[\frac{\mathrm{K}_{1}+2 \mathrm{~K}_{2}}{2\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}\right]

For CB\mathrm{C}_{\mathrm{B}} :

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CB=K2C2+K1 K2C K1+K2=K2C[ K1+2 K22( K1+K2)]\begin{aligned} \mathrm{C}_{\mathrm{B}} & =\frac{\mathrm{K}_{2} \mathrm{C}}{2}+\frac{\mathrm{K}_{1} \mathrm{~K}_{2} \mathrm{C}}{\mathrm{~K}_{1}+\mathrm{K}_{2}} & =\mathrm{K}_{2} \mathrm{C}\left[\frac{\mathrm{~K}_{1}+2 \mathrm{~K}_{2}}{2\left(\mathrm{~K}_{1}+\mathrm{K}_{2}\right)}\right] \end{aligned} For CC\mathrm{C}_{\mathrm{C}} : CC=2 K1 K2C(K1+K2)\mathrm{C}_{\mathrm{C}}=\frac{2 \mathrm{~K}_{1} \mathrm{~K}_{2} \mathrm{C}}{\left(\mathrm{K}_{1}+\mathrm{K}_{2}\right)} CA>CC>CB\mathrm{C}_{\mathrm{A}}>\mathrm{C}_{\mathrm{C}}>\mathrm{C}_{\mathrm{B}}

Solution figure

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Subject
Physics
Chapter
Capacitors and R-C Circuits
Topic
Effect of Dielectrics