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Induced emf or current when the flux is a given function of time

This type of question, asked 5 times: 16 May 2023 S1, 9 May 2024 S1, 22 Apr 2025 S1, 19 Apr 2026 S1, 13 May 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    16 May 2023 S1

    43
    A coil of resistance 250 Ω250\,\Omega is placed in a magnetic field. If the magnetic flux (ϕ\phi) linked with the coil varies with time t (s) as ϕ=50t2+7\phi = 50t^2 + 7. The current in the coil at t=4 st = 4\,\text{s} is

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  2. Question 2

    9 May 2024 S1

    8
    The magnetic flux through a loop of resistance 10 Ω10\,\Omega is varying according to the relation ϕ=6t2+7t+1\phi=6t^2+7t+1, where ϕ\phi is in milliweber, time is in second. Then at time t=1t=1 s the induced e.m.f. is

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  3. Question 3

    22 Apr 2025 S1

    50
    A coil of resistance 400Ω400\Omega is placed in a magnetic field. If the magnetic flux ' ϕ\phi, (Wb) linked with the coil varies with time ' tt ' ( ss ) as ϕ=50t2+4\phi= 50t^{2}+ 4, the current in the coil at t=2 st = 2\text{ }s will be

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  4. Question 4

    19 Apr 2026 S1

    136
    Magnetic flux linked with the coil in weber is given by the equation Φ=5t2+6t+11\Phi = 5t^2 + 6t + 11. The e.m.f. induced in the coil in the 5th5^{th} second will be

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  5. Question 5

    13 May 2026 S2

    134
    A varying magnetic flux linking a coil is Φ=xt2\Phi = xt^2. If at time t=3t = 3 s, the e.m.f. induced is 99V then the magnitude of xx is (in Wb/s2\mathrm{Wb/s^2})

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