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A coil of resistance 400Ω is placed in a magnetic field. If the magnetic flux Φ (wb) linked with the coil varies with time t (sec) as Φ = 50t² + 4. The current in the coil at t = 2 sec is

  1. 0.5 A
  2. 0.1 A
  3. 2 A
  4. 1 A

Correct answer: 0.5 A

Solution

The induced EMF is given by Faraday's law as E = -dΦ/dt. Differentiating Φ = 50t² + 4, we get dΦ/dt = 100t. At t = 2 s, dΦ/dt = 100 × 2 = 200 V. The current is I = E/R = 200/400 = 0.5 A.

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