FCC Exam Question: 6A88

What is the total reactance of a series AC circuit, with no resistance and equal inductance and capacitivereactances?

A. The two reactances cancel being equal and opposite
B. Net impedance is purely resistive and contains no reactive component
C. The total reactance is zero at the resonant frequency
D. All of the above
Correct Answer: D

Explanation: In a series AC circuit, inductive reactance ($X_L$) and capacitive reactance ($X_C$) are opposite in phase. When they are equal in magnitude, they cancel each other out. A) If $X_L = X_C$, the total reactance ($X_{total} = X_L - X_C$) becomes zero. This confirms that the two reactances cancel. B) Impedance ($Z$) is given by $Z = R + jX_{total}$. Since there is no resistance ($R=0$) and $X_{total}=0$, the net impedance is $Z = 0 + j0 = 0$. An impedance of zero has no reactive component and can be considered purely resistive (or purely non-reactive). C) The condition where the inductive and capacitive reactances are equal ($X_L = X_C$) is the definition of a series resonant circuit. At resonance, the total reactance of the circuit is indeed zero. Therefore, all the statements accurately describe the conditions and consequences of a series AC circuit with no resistance and equal inductance and capacitive reactances.

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