Answer: f0 = 1/(2π√(LC)).
- A f0 = 1/(2π√(LC))
- B f0 = 2π√(LC)
- C f0 = LC/2π
- D f0 = 2πLC
Correct answer: A. f0 = 1/(2π√(LC))
Explanation: At resonance: XL = XC → ωL = 1/(ωC) → ω² = 1/(LC) → f0 = 1/(2π√(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.