For a series RLC circuit at resonance, the impedance magnitude is

For a series RLC circuit at resonance, the impedance magnitude is

• A. Z = R
• B. Z = 0
• C. Z = ∞
• D. Z = jR

Answer: (A)

At resonance in a series RLC circuit, the inductive and capacitive reactances cancel each other out. The total impedance is Z = R + j(X_L − X_C). When ωL = 1/(ωC), the imaginary part becomes zero, so Z = R, a purely real impedance. Therefore, the magnitude is |Z| = R. The other possibilities would imply zero, infinite, or purely imaginary impedance, which do not occur at resonance in this setup.

At resonance in a series RLC circuit, the inductive and capacitive reactances cancel each other out. The total impedance is Z = R + j(X_L − X_C). When ωL = 1/(ωC), the imaginary part becomes zero, so Z = R, a purely real impedance. Therefore, the magnitude is |Z| = R. The other possibilities would imply zero, infinite, or purely imaginary impedance, which do not occur at resonance in this setup.