Question 3-29D2

In a series R-L-C circuit, the total impedance ($Z$) is calculated as $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $R$ is resistance, $X_L$ is inductive reactance, and $X_C$ is capacitive reactance. At resonance, the defining condition is that the inductive reactance ($X_L$) precisely equals the capacitive reactance ($X_C$). Because these reactances are 180 degrees out of phase, they effectively cancel each other out. When $X_L = X_C$, the $(X_L - X_C)$ term in the impedance formula becomes zero. The formula then simplifies to $Z = \sqrt{R^2 + 0^2} = \sqrt{R^2} = R$. Therefore, at series resonance, the total impedance of the circuit is at its minimum value and is approximately equal to the circuit's ohmic resistance. A) Is incorrect because high impedance is characteristic of a *parallel* R-L-C circuit at resonance. C) and D) Are incorrect because at resonance, the inductive and capacitive reactances cancel each other out, so the total impedance is not dominated by either reactive component.