Answer: Equal in magnitude and opposite in phase (cancel).
- A Equal in magnitude and opposite in phase (cancel)
- B Equal in magnitude and same phase (add) according to standard textbooks
- C Zero in general practice as frequently described
- D Both equal to source voltage in most textbook accounts
Correct answer: A. Equal in magnitude and opposite in phase (cancel)
Explanation: At resonance, V<sub>L</sub> = IX_L and V<sub>C</sub> = IX_C. Since X<sub>L</sub> = X<sub>C</sub>, |V<sub>L</sub>| = |V<sub>C</sub>|. But they are 180° out of phase with each other (V<sub>L</sub> leads I by 90°, V<sub>C</sub> lags I by 90°), so they cancel in series.
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.