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Capacitor filled with two or more dielectric slabs: combine the parts in series and parallel

This type of question, asked 4 times: 2021 Paper 19, 3 Apr 2025, 23 Jan 2026 S1, 24 Jan 2026 S2. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 19

    10
    A parallel - plate capacitor with plate area AA has separation d between the plates. Two dielectric slabs of dielectric constant K1K_{1} and K2K_{2} of same area A/2A/2 and thickness d/2d/2 are inserted in the space between the plates. The capacitance of the capacitor will be given by:

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  2. Question 2

    3 Apr 2025

    8
    A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant ε1\varepsilon_{1} and ε2\varepsilon_{2}, as shown in figures. The distance between the plates is d and area of each plate is A . If capacitance in first configuration and second configuration are C1C_{1} and C2C_{2} respectively, then C1C2\frac{C_{1}}{C_{2}} is:

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  3. Question 3

    23 Jan 2026 S1

    25
    The space between the plates of a parallel-plate capacitor of capacitance C (without any dielectric) is now filled with three dielectric slabs of dielectric constants K1=2, K2=3K_{1} = 2,{\text{ }K}_{2} = 3, and K3=5K_{3} = 5 (as shown in the figure). If new capacitance is n3C\frac{n}{3}C then the value of nn is ____\_\_\_\_ .
  4. Question 4

    24 Jan 2026 S2

    10
    Three parallel plate capacitors each with area A and separation d are filled with two dielectric ( k1k_{1} and k2k_{2} ) in the following fashion. Which of the following is true? (k1>k2)\left( k_{1}>k_{2} \right)

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