FCC Exam Question: 6A112

The total impedance of a series AC circuit with an inductive reactance of 24 ohms, a resistance of 16ohms, and a capacitive reactance of 16 ohms is:

A. 20 ohms
B. 16 ohms
C. 10 ohms
D. None of the above
Correct Answer: B

Explanation: 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.

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Includes Elements 1, 3, 6, 7R, 8, and 9.