A periodic current is described by i = I₀(1 + sinωt). Which of the following statements are correct when the current is observed over one complete cycle?
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Question

A periodic current is described by i = I₀(1 + sinωt). Which of the following statements are correct when the current is observed over one complete cycle?

G1 Physics · Accepted Answer

Over a complete cycle, ⟨sinωt⟩ = 0 and ⟨sin²ωt⟩ = 1/2. Thus Iₐᵥg = I₀ and Iᵣₘₛ² = I₀²(1 + 1/2) = 3I₀²/2. Also, 1 + sinωt ranges from 0 to 2, so the current is never negative.