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Growth of current in an LR circuit: energy stored or its rate at an instant

This type of question, asked 3 times: 2021 Paper 10, 13 Apr 2023, 22 Jan 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 10

    16
    The time taken for the magnetic energy to reach 25%25\% of its maximum value, when a solenoid of resistance RR, inductance LL is connected to a battery, is:

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  2. Question 2

    13 Apr 2023

    27
    In the given figure, an inductor and a resistor are connected in series with a battery of emf EE volt. Ea2 b J/s\frac{E^{a}}{2\text{ }b}\text{ }J/s represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of ba\frac{b}{a} will be
  3. Question 3

    22 Jan 2026 S1

    25
    Inductance of a coil with 10410^{4} turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of 10Ω10\Omega. The energy density in the inductor when the current reaches (1e)\left( \frac{1}{e} \right) of its maximum value is απ×1e2 J/m3\alpha\pi \times \frac{1}{e^{2}}\text{ }J/m^{3}. The value of α\alpha is ____\_\_\_\_ . (μ0=4π×10−7Tm/A)\left( \mu_{0} = 4\pi \times 10^{- 7}Tm/A \right).