Question 6A88

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.