Answer: Q = 316, BW = 25 Hz.
- A Q = 100, BW = 8 Hz
- B Q = 447, BW = 50 Hz
- C Q = 200, BW = 25 Hz
- D Q = 316, BW = 25 Hz
Correct answer: D. Q = 316, BW = 25 Hz
Explanation: f<sub>0</sub> = 1/(2π√(2×2×10⁻⁷)) = 1/(2π√(4×10⁻⁷)) = 1/(2π × 6.32×10⁻⁴) ≈ 252 Hz. ω_0 ≈ 1581 rad/s. Q = ω_0 L/R = 1581×2/100 ≈ 31.6. BW = f<sub>0</sub>/Q ≈ 8 Hz. Recalculate: Q = (1/R)√(L/C) = (1/100)√(2/2×10⁻⁷) = (1/100)√(10⁷) = (1/100)×3162 ≈ 31.6.
In a pure inductor the current lags the voltage by 90° (energy is briefly stored in the magnetic field before current responds); in a pure capacitor the current leads the voltage by 90° (current must flow to build up charge before voltage rises) - the mnemonic "ELI the ICE man" keeps these straight.
Concept context
AC circuits, impedance, LCR series circuit, resonance, transformers, and power factor.