A series AC circuit has resistance 1 kΩ, capacitance 0.1 μF and inductance 1 mH. Find the approximate resonance frequency.
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Question

A series AC circuit has resistance 1 kΩ, capacitance 0.1 μF and inductance 1 mH. Find the approximate resonance frequency.

G1 Physics · Accepted Answer

Step 1: Series resonance occurs when inductive and capacitive reactances cancel: ω₀L = 1/(ω₀C). Step 2: ω₀ = 1/√(LC), so f₀ = 1/(2π√(LC)). Step 3: Convert units: L = 1 mH = 10⁻³ H; C = 0.1 μF = 10⁻⁷ F. Step 4: LC = 10⁻¹⁰, and √(LC) = 10⁻⁵. Step 5: f₀ = 1/(2π × 10⁻⁵) ≈ 1.59 × 10⁴ Hz = 15.9 kHz. Final answer: 15.9 kHz (Option A).