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New capacitance when plate size, separation or the dielectric is changed

This type of question, asked 4 times: 3 May 2023 S1, 13 May 2024 S2, 13 Apr 2026 S2, 18 Apr 2026 S1. All 4 questions below, oldest first.

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  1. Question 1

    3 May 2023 S1

    24
    Two circular metal plates each of radius rr are kept parallel to each other at a distance dd apart. The capacitance of the capacitor formed is C1C_1. If the radius of each plate is increased to 2\sqrt{2} times the earlier radius and their separation is decreased to half the initial value, the capacitance becomes C2C_2. The ratio of the capacitances C1:C2C_1 : C_2 is

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  2. Question 2

    13 May 2024 S2

    36
    In a parallel plate capacitor with air between the plates, the distance 'dd' between the plates is changed and the space is filled with dielectric constant 8. The capacity of the capacitor is increased 16 times, the distance between the plates is

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  3. Question 3

    13 Apr 2026 S2

    129
    A parallel plate capacitor with air between the plate has a capacitance of 1515 pF. The separation between the plates becomes twice and the space between them is filled with a medium of dielectric constant 3.53.5. Then the capacitance becomes x/4x/4 pF. The value of xx is

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  4. Question 4

    18 Apr 2026 S1

    128
    Two circular plates each of radius 'rr' are kept parallel to each other distance 'dd' apart. The capacitance of the capacitor formed is 'C1C_1'. If the radius of each of the plates is increased to 3\sqrt{3} times the earlier radius and their distance of separation decreased to half the initial value, the capacitance now becomes 'C2C_2'. The ratio C1:C2C_1 : C_2 is

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