In a series circuit containing a resistor, inductor, and capacitor at resonance, what happens to the reactive part of the impedance?

• A. X_L = X_C, so reactive parts cancel and Z ≈ R
• B. X_L > X_C, so Z is dominated by XL
• C. X_L < X_C, so Z is dominated by XC
• D. Z becomes infinite

Answer: (A)

In a series circuit with a resistor, inductor, and capacitor, resonance occurs when the inductive and capacitive reactances balance each other so their net reactive effect is zero. The total impedance is Z = R + j(X_L − X_C). At resonance, X_L = X_C, so the imaginary part is zero and Z reduces to R. This means the circuit behaves as a purely resistive load at the resonance frequency, with the current determined by the resistance and no net reactive energy storage over a cycle.

If X_L were greater than X_C, the circuit would appear inductive; if X_L were less than X_C, it would appear capacitive. In either case, there would be a nonzero reactive component, not the purely resistive result seen at resonance. The impedance being infinite would not occur in a series R-L-C circuit with a resistor; the current would still flow limited by the resistance.