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Same capacitors joined in series and in parallel: ratio of equivalent capacitance or stored energy

This type of question, asked 3 times: 2021 Paper 1, 2021 Paper 25, 5 Apr 2024. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 1

    4
    Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be -

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  2. Question 2

    2021 Paper 25

    18
    Consider the combination of 2 capacitors C1C_{1} and C2C_{2}, with C2>C1C_{2}>C_{1}, when connected in parallel, the equivalent capacitance is 154\frac{15}{4} times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, C2C1\frac{C_{2}}{C_{1}}.

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  3. Question 3

    5 Apr 2024

    30
    Three capacitors of capacitances 25μF,30μF25\mu F,30\mu F and 45μF45\mu F are connected in parallel to a supply of 100 V. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is 9xE\frac{9}{x}E. The value of xx is..........