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The magnetic flux linked with a coil is given by Φ(t) = (2t² + 2t + 1) Wb and its resistance is 10 Ω. The current passing through the coil at t = 2 s is _______ A.

Asked in GSEB Board March 2023 · Induced current, heat and power

• (1) 1.5
• (2) 1
• (3) 0.5
• (4) 2

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 1.5 A. Sanity check: (dΦ)/(dt) = 4t + 2 = 10 V at t = 2 s, and (10)/(10) = 1 A; 1.5 A would need an emf of 15 V.
• (3) No single slip gives 0.5 A; it would need an emf of 5 V. At t = 2 s the flux changes at 4(2) + 2 = 10 Wb s⁻¹, which is 10 V.
• (4) No single slip gives 2 A; that would need (dΦ)/(dt) = 20 V. The emf is 10 V, and 10 V across 10 Ω drives 1 A.

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