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Charging or discharging a capacitor through a resistor: time, resistance or capacitance from the exponential

This type of question, asked 4 times: 2021 Paper 16, 2021 Paper 24, 29 Jun 2022, 5 Apr 2024. All 5 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 16

    10
    The switch is closed at t=0t = 0. Find time after which voltage across capacitor becomes 50 volt. [take ln⁡2=0.6\ln2 = 0.6 ]

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  2. Question 2

    2021 Paper 16

    2
    A capacitor of capacitance 100μF100\mu F discharges through a resistor R. At the same time a radioactive substance decays with mean life 30 ms30\text{ }ms. If ratio of charge on capacitor to activity of substance does not change with time, then find RR.

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  3. Question 3

    2021 Paper 24

    17
    A capacitor is connected to a 20 V20\text{ }V battery through a resistance of 10Ω10\Omega. It is found that the potential difference across the capacitor rises to 2 V2\text{ }V in 1μs1\mu s. The capacitance of the capacitor is ____\_\_\_\_ μF\mu F. Given: ln⁡(109)=0.105\ln\left( \frac{10}{9} \right)= 0.105

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  4. Question 4

    29 Jun 2022

    97
    A capacitor is discharging through a resistor RR. Consider in time t1t_{1}, the energy stored in the capacitor reduces to half of its initial value and in time t2t_{2}, the charge stored reduces to one eighth of its initial value. The ratio t1/t2t_{1}/t_{2} will be:

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  5. Question 5

    5 Apr 2024

    23
    The electric field between the two parallel plates of a capacitor of 1.5μF1.5\mu F capacitance drops to one third of its initial value in 6.6μs6.6\mu s when the plates are connected by a thin wire. The resistance of this wire is ................ Ω\Omega. (Given, log⁡3=1.1\log3 = 1.1 )