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Question

A solenoid of 600 turns and length 0.8 m induces an emf of 2 V in a nearby coil when its current
changes from 1 A to 4 A in 0.2 s. What is the mutual inductance?

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Explanation

**Mutual inductance calculation** M = e₂/(dI₁/dt), for 200 turns length 0.5 m nearby coil e=0.5 V dI=2 A dt=0.2 s dI/dt=10 A/s, M=0.5/10=0.05 H, depends on geometry, orientation, number of turns, area, separation, coupling coefficient k = M/√(L₁ L₂) ≤1. ε = M (Δ I/Δ t) . Δ I = 4 - 1 = 3 A , Δ t = 0.2 s . M = (ε/(Δ I/Δ t)) = (2/(3/0.2)) = (2/15) = 0.133 H ≈ 0.13 H . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L =

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