Answer: X L = 31.4 Ω, X C = 31.8 Ω.
- A X<sub>L</sub> = 3.14 Ω, X<sub>C</sub> = 31.8 Ω
- B X<sub>L</sub> = 31.4 Ω, X<sub>C</sub> = 31.8 Ω
- C X<sub>L</sub> = 314 Ω, X<sub>C</sub> = 3.18 Ω
- D X<sub>L</sub> = 3.14 Ω, X<sub>C</sub> = 318 Ω
Correct answer: B. X<sub>L</sub> = 31.4 Ω, X<sub>C</sub> = 31.8 Ω
Explanation: X<sub>L</sub> = 2πfL = 2π × 50 × 0.01 = π ≈ 3.14 Ω. Wait: 2 × 3.14 × 50 × 0.01 = 3.14 Ω. X<sub>C</sub> = 1/(2πfC) = 1/(2π × 50 × 10⁻⁴) = 1/(0.03142) = 31.8 Ω. So option A is correct.
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.