Answer: 287 Ω.
- A √(20² + (31.4-318.3)²) Ω ≈ 287 Ω
- B 20 Ω
- C 100 Ω
- D 287 Ω
Correct answer: D. 287 Ω
Explanation: X<sub>L</sub> = 2π×50×0.1 = 31.4 Ω. X<sub>C</sub> = 1/(2π×50×10⁻⁵) = 318.3 Ω. Z = √(400 + (31.4-318.3)²) = √(400 + 82369) ≈ √82769 ≈ 287.7 Ω.
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.