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Flux varies as phi = 50t^2 + c through a coil of given resistance: current at a given time

The same question, asked 2 times: 16 May 2023 S1*, 22 Apr 2025 S1. Every wording 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

    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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