Inductive & Capacitive Reactance — A/L Physics

How do I practise Inductive & Capacitive Reactance?

1 question with a worked solution

1. In a series LCR alternating current circuit, an inductor of inductance L = 0.10 H and a capacitor of capacitance C = 10 μF are connected with a resistor. What is the electrical resonant frequency f₀ of the circuit?
   1. A) 50 Hz
   2. B) 1000 Hz
   3. C) 318 Hz
   4. D) 159 Hz
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   Correct answer: D) 159 Hz

   Resonance occurs when inductive reactance equals capacitive reactance: X_L = X_C => ω₀ L = 1 / (ω₀ C) => f₀ = 1 / (2π √(LC)). Substituting: f₀ = 1 / [2π √(0.10 × 10 × 10⁻⁶)] = 1 / [2π √(10⁻⁶)] = 1 / [2π × 10⁻³] = 1000 / (2π) ≈ 159.15 Hz.

   Show worked solution

   Step 1: Formula: f₀ = 1 / (2π √(LC)). Step 2: √(LC) = √(0.10 × 10 × 10⁻⁶) = √(10⁻⁶) = 10⁻³ s. Step 3: f₀ = 1 / (2π × 10⁻³) = 1000 / 6.283 ≈ 159.2 Hz. Answer: 159 Hz.
   Modelled on: the A/L Physics examination pattern

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Where does Inductive & Capacitive Reactance fit in the syllabus?

Unit 8.5 · Year 2 · Term 1