Answer: √(R² + (X L - X C )²).
- A √(R² + (X<sub>L</sub> - X<sub>C</sub>)²)
- B R + X<sub>L</sub> + X<sub>C</sub>
- C R + X<sub>L</sub> - X<sub>C</sub>
- D √(R² + X<sub>L</sub>² + X<sub>C</sub>²)
Correct answer: A. √(R² + (X<sub>L</sub> - X<sub>C</sub>)²)
Explanation: In series LCR, X<sub>L</sub> and X<sub>C</sub> are out of phase with each other. Z = √(R² + (X<sub>L</sub> - X<sub>C</sub>)²). When X<sub>L</sub> = X<sub>C</sub>, Z = R (resonance).
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.