Answer: X L = X C (inductive reactance equals capacitive reactance).
- A X<sub>L</sub> = X<sub>C</sub> (inductive reactance equals capacitive reactance)
- B R = X<sub>L</sub>, when resistance equals inductive reactance
- C R = X<sub>C</sub>, when resistance equals capacitive reactance
- D Z = 0, when the total impedance vanishes entirely
Correct answer: A. X<sub>L</sub> = X<sub>C</sub> (inductive reactance equals capacitive reactance)
Explanation: At resonance, X<sub>L</sub> = X<sub>C</sub>, so the reactances cancel. Z = R (minimum), current is maximum. Resonant frequency ω_0 = 1/√(LC).
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.