A parallel resonant circuit (tank circuit) contains an inductor of 10 mH and a capacitor of 40 μF. What is the approximate resonant frequency f0 of this circuit?
Answer and explanation
Correct answer: A. 252 Hz
- Step 1: Resonant frequency formula: f0 = 1 / (2π √(L C)). Step 2. Compute product: L C = (10 × 10⁻³) × (40 × 10⁻⁶) = 4.0 × 10⁻⁷. Step 3. Take square root: √(4.0 × 10⁻⁷) = √(40 × 10⁻⁸) ≈ 6.325 × 10⁻⁴. Step 4. Compute f0: 1 / (2 × 3.142 × 6.325 × 10⁻⁴) = 1 / (3.974 × 10⁻³) ≈ 251.6 Hz ≈ 252 Hz. Answer: 252 Hz. Why not the others: 503 Hz forgets the factor of 2 in 2π; 126 Hz halves the frequency; 398 Hz is an arithmetic error.
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