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Induced current from a given flux-time (or field-time) relation

This type of question, asked 5 times: 2021 Paper 17, 26 Jun 2022, 25 Jul 2022, 31 Jan 2024, 5 Apr 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 17

    24
    In the given figure the magnetic flux through the loop increases according to the relation ϕB(t)=10t2+20t\phi_{B}(t) = 10t^{2} + 20t, where ϕB\phi_{B} is in milliwebers and tt is in seconds. The magnitude of current through R=2ΩR = 2\Omega resistor at t=5 st = 5\text{ }s is mAmA.

  2. Question 2

    26 Jun 2022

    12
    The magnetic flux through a coil perpendicular to its plane is varying according to the relation ϕ=\phi = (5t3+4t2+2t−5)\left( 5t^{3}+ 4t^{2} + 2t - 5 \right) Weber. If the resistance of the coil is 5ohm5ohm, then the induced current through the coil at t=2sect = 2sec will be:

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  3. Question 3

    25 Jul 2022

    120
    Magnetic flux (in weber) in a closed circuit of resistance 20Ω20\Omega varies with time t(s)t\left( s \right) as ϕ=8t2−9t+5\phi= 8t^{2}- 9t+ 5. The magnitude of the induced current at t=0.25 st = 0.25\text{ }s will be ____\_\_\_\_ mA.

  4. Question 4

    31 Jan 2024

    113
    The magnetic flux ϕ\phi (in weber) linked with a closed circuit of resistance 8Ω8\Omega varies with time (in seconds) as ϕ=5t2−36t+1\phi= 5t^{2}- 36t + 1. The induced current in the circuit at t=2 st= 2\text{ }s is _____ A.

  5. Question 5

    5 Apr 2026 S2

    25
    A circular loop of radius 20 cm and resistance 2Ω2\Omega is placed in a time varying magnetic field B→=(2t2+2t+3)T\overrightarrow{B} = \left( 2t^{2} + 2t + 3 \right)T. The plane of the loop is perpendicular to the magnetic field. The induced current in the loop at t=3 st = 3\text{ }s is α50 A\frac{\alpha}{50}\text{ }A. The value of α\alpha is ____\_\_\_\_ (Take π=22/7\pi = 22/7 )