In a series RLC circuit, when X_L equals X_C, the impedance is purely real and equals which value?

In a series RLC circuit, when X_L equals X_C, the impedance is purely real and equals which value?

• A. Z = 0
• B. Z = jR
• C. Z = R
• D. Z = R + jX

Answer: (C)

When the inductive and capacitive reactances cancel in a series RLC circuit, the reactive part of the impedance disappears. The total impedance is Z = R + j(X_L − X_C). At resonance, X_L = X_C, so the imaginary part is zero and Z reduces to Z = R, a purely real (resistive) value. The magnitude is simply R, and there’s no phase shift from reactance. Other options would imply a remaining imaginary component or zero impedance, which doesn’t happen at resonance unless the resistance itself is zero.

When the inductive and capacitive reactances cancel in a series RLC circuit, the reactive part of the impedance disappears. The total impedance is Z = R + j(X_L − X_C). At resonance, X_L = X_C, so the imaginary part is zero and Z reduces to Z = R, a purely real (resistive) value. The magnitude is simply R, and there’s no phase shift from reactance. Other options would imply a remaining imaginary component or zero impedance, which doesn’t happen at resonance unless the resistance itself is zero.