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Capacitance with a dielectric slab or metal sheet thinner than the plate gap

This type of question, asked 9 times: 2021 Paper 5, 25 Jun 2022, 28 Jul 2022, 25 Jan 2023, 6 Apr 2023, 10 Apr 2023, 8 Apr 2024, 21 Jan 2026 S1, 23 Jan 2026 S2. All 10 questions below, oldest first.

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  1. Question 1

    2021 Paper 5

    2
    For changing the capacitance of a given parallel plate capacitor, a dielectric material of dielectric constant KK is used, which has the same area as the plates of the capacitor. The thickness of the dielectric slab is 34 d\frac{3}{4}\text{ }d, where ' dd ' is the separation between the plates of parallel plate capacitor. The new capacitance ( C′C^{'} ) in terms of original capacitance (C0)\left( C_{0} \right) is given by the following relation :

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  2. Question 2

    25 Jun 2022

    98
    Two metallic plates form a parallel plate capacitor. The distance between the plates is ' dd '. A metal sheet of thickness d2\frac{d}{2} and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

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  3. Question 3

    28 Jul 2022

    99
    A slab of dielectric constant KK has the same crosssectional area as the plates of a parallel plate capacitor and thickness 34 d\frac{3}{4}\text{ }d, where dd is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be: (Given Co=C_{o}= capacitance of capacitor with air as medium between plates.)

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  4. Question 4

    25 Jan 2023

    16
    A parallel plate capacitor has plate area 40 cm240{\text{ }cm}^{2} and plates separation 2 mm2\text{ }mm. The space between the plates is filled with a dielectric medium of a thickness 1 mm1\text{ }mm and dielectric constant 5. The capacitance of the system is:

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  5. Question 5

    25 Jan 2023

    119
    A capacitor has capacitance 5μF5\mu F when its parallel plates are separated by air medium of thickness dd. A slab of material of dielectric constant 1.5 having area equal to that of plates but thickness d2\frac{d}{2} is inserted between the plates. Capacitance of the capacitor in the presence of slab will be ___ μF\mu F.

  6. Question 6

    6 Apr 2023

    30
    A parallel plate capacitor with plate area AA and plate separation dd is filled with a dielectric material of dielectric constant K=4K = 4. The thickness of the dielectric material is xx, where x<dx < d. Let C1C_{1} and C2C_{2} be the capacitance of the system for x=13 dx =\frac{1}{3}\text{ }d and x=2 d3x =\frac{2\text{ }d}{3}, respectively. If C1=2μFC_{1}= 2\mu F the value of C2C_{2} is___ μF\mu F

  7. Question 7

    10 Apr 2023

    96
    The distance between two plates of a capacitor is dd and its capacitance is C1C_{1}, when air is the medium between the plates. If a metal sheet of thickness 2 d3\frac{2\text{ }d}{3} and of same area as plate is introduced between the plates, the capacitance of the capacitor becomes C2C_{2}. The ratio C2C1\frac{C_{2}}{C_{1}} is:

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  8. Question 8

    8 Apr 2024

    103
    A capacitor has air as dielectric medium and two conducting plates of area 12 cm212{\text{ }cm}^{2} and they are 0.6 cm0.6\text{ }cm apart. When a slab of dielectric having area 12 cm212{\text{ }cm}^{2} and 0.6 cm0.6\text{ }cm thickness is inserted between the plates, one of the conducting plates has to be moved by 0.2 cm0.2\text{ }cm to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given ϵ0=8.834×10−12 F/m\epsilon_{0}= 8.834 \times10^{- 12}\text{ }F/m )

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  9. Question 9

    21 Jan 2026 S1

    9
    A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness (13)rd \left( \frac{1}{3} \right)^{\text{rd~}} of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

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  10. Question 10

    23 Jan 2026 S2

    9
    A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws 25%25\% more charge from the battery. The dielectric constant of mica is ____\_\_\_\_ .

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