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Energy stored in an inductor carrying a current

This type of question, asked 3 times: 2021 Paper 18, 25 Jun 2022, 11 Apr 2023. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 18

    7
    An inductor coil stores 64 J64\text{ }J of magnetic field energy and dissipates energy at the rate of 640 W640\text{ }W when a current of 8 A8\text{ }A is passed through it. If this coil is joined across an ideal battery, find the time constant of the circuit in seconds:

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  2. Question 2

    25 Jun 2022

    29
    The current in a coil of self- inductance 2.0H2.0H is increasing according to I=2sin⁡(t2)AI= 2\sin\left( t^{2} \right)A. The amount of energy spent during the period when current changes from 0 to 2 A2\text{ }A is ____\_\_\_\_ J.

  3. Question 3

    11 Apr 2023

    116
    A coil has an inductance of 2H2H and resistance of 4Ω4\Omega. A 10 V10\text{ }V is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be __×10−2 J\times10^{- 2}\text{ }J