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A solenoid having inductance 4.0 H and resistance 10 Ω is connected to a 4.0 V battery at t = 0. Find (a) the time constant, (b) the time elapsed before the current reaches 0.63 of its steady-state value, (c) the power delivered by the battery at this instant and (d) the power dissipated in Joule heating at this instant.

Jitender Pal
7 years ago
Sol. L = 4.0 H, R = 10 Ω, E = 4 V a) Time constant = τ = L/R = 4/10 = 0.4 s. b) i = 0.63 i0 Now, 0.63 i0 = i0 (1 – e^–t/τ) ⇒ e–t/τ = 1 – 0.63 = 0.37 ⇒ ℓ ne^–t/τ = In 0.37 ⇒ –t/τ = –0.9942 ⇒ t = 0.9942 x 0.4 = 0.3977 = 0.40 s. c) i = i0 (1 – e^–t/τ) ⇒ 4/10 (1 – e^-0.4/0.4) = 0.4 x 0.6321 = 0.2528 A. Power delivered = VI = 4 x 0.2528 = 1.01 = 1ω. d) Power dissipated in Joule heating =I^2R = (0.2528)2 x 10 = 0.639 = 0.64 ω.