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The mutual inductance of a system of two coils is 5 mH. The current in the first coil varies according to the equation I = I₀ sin ω t, where I₀ = 10 A and ω = 100π rad s⁻¹. The maximum value of the induced emf in the second coil is ______.

Asked in GSEB Board March 2018 · Mutual inductance and induced EMF

• (1) 2π V
• (2) 5π V
• (3) π V
• (4) 4π V

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 2π V. Sanity check: the peak emf is MI₀ω = 5×10⁻³×10×100π = 5π V; 2π V would need M = 2 mH.
• (3) No single slip gives π V. It would need MI₀ = 0.01 Wb (for example I₀ = 2 A), but here MI₀ = 5×10⁻³×10 = 0.05 Wb.
• (4) No single slip gives 4π V. The largest value of cos ω t is exactly 1, so nothing reduces the peak below MI₀ω = 5π V; 4π V would need M = 4 mH.

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