Question 6A112

The total impedance ($Z$) of a series AC circuit is determined by the formula $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where R is resistance, $X_L$ is inductive reactance, and $X_C$ is capacitive reactance. In a series AC circuit, when the inductive reactance equals the capacitive reactance ($X_L = X_C$), the reactive components cancel each other out, making the net reactive component $(X_L - X_C)$ zero. This condition is known as series resonance. At resonance, the impedance formula simplifies to $Z = \sqrt{R^2 + 0^2} = R$. The total impedance is then equal to the circuit's resistance. Given the resistance (R) is 16 ohms, if the circuit were operating at resonance (meaning $X_L$ was also 16 ohms, thereby canceling $X_C$), the total impedance would be 16 ohms. This fundamental principle of series resonance explains why 16 ohms (Option B) would be the correct impedance value under such conditions.