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Change in capacitance when a slab fills a fraction of the gap

The same question, asked 3 times: 16 Apr 2026 S2*, 19 Apr 2026 S1*, 13 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    16 Apr 2026 S2

    128
    A capacitor has capacity C when it's parallel plates are separated by air medium of thickness 'd'. A slab of material of dielectric constant K having area equal to that of plates but thickness d2\dfrac{d}{2} is inserted between the plates. Capacitance of the capacitor in the presence of slab will be

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  2. Question 2

    19 Apr 2026 S1

    126
    A slab of material of dielectric constant KK has the same area as the plates of a parallel plate capacitor but has a thickness (4/5)d(4/5)d, where dd is the separation of the plates. The capacitance in the presence and absence of dielectric are CC and C0C_0 respectively. The ratio (C/C0)(C/C_0) is

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  3. Question 3

    13 May 2026 S2

    128
    A slab of material of dielectric constant kk has the same area as the plates of the parallel plate capacitor but has thickness 3d4\dfrac{3d}{4}, where dd is the separation of the plates. How is the capacitance changed, when the slab is inserted between the plates? (CC = original capacitance)

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