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q = CV₁ cos ωt. i = -ωCV₁ sin ωt. Also, ω² = 1 / LC and V = V₁ cos ωt. At t = t₁, V = V₂ and i = -ωCV₁ sin ωt₁. cos ωt₁ = V₂ / V₁. Hence, i = V₁ √(C / L) √(1 - (V₂² / V₁²)).

1. i = (C(V₁² - V₂²) / L)^(1/2)
2. i = (C(V₁² + V₂²) / L)^(1/2)
3. i = (C(V₁² - V₂²) / L)^(1/3)
4. i = (C(V₁² + V₂²) / L)^(1/3)

Correct answer: i = (C(V₁² - V₂²) / L)^(1/2)

Solution

The given expression for current is derived using the relationship between charge, current, and voltage in an LC circuit. Substituting cos(ωt₁) = V₂ / V₁ into the expression for current and simplifying leads to the result i = (C(V₁² - V₂²) / L)^(1/2).

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