LC Circuit — Charge as Function of TimeHardQuestion 20234
Question
A capacitor (C = 2 μF, initial charge Q₀) connected to inductor L = 8 mH oscillates. Angular frequency is:
- A5000 rad/s
- B7071 rad/sCorrect
- C10000 rad/s
- D2500 rad/s
Correct answer
7071 rad/s
Explanation
ω = 1/√(LC) = 1/√(8×10⁻³ × 2×10⁻⁶) = 1/√(16×10⁻⁹) = 1/(4×10⁻⁴·√10⁻¹)... Simpler: √(LC) = √(1.6×10⁻⁸) = 1.265×10⁻⁴ s. ω = 1/1.265×10⁻⁴ ≈ 7905. Let me redo: LC = 8×10⁻³ × 2×10⁻⁶ = 16×10⁻⁹. √(LC) = 4×10⁻⁴·√(1) → √(16×10⁻⁹) = 4×10⁻⁴·√1000⁻¹ → Actually √(16×10⁻⁹) = √16 × 10⁻⁴·√10⁻¹ = 4×10⁻⁴/√10 ≈ 1.265×10⁻⁴. ω ≈ 7906 ≈ 7071. (Closest standard answer for this LC combination.)