Which option correctly describes the reactive part of the series RLC impedance?

Which option correctly describes the reactive part of the series RLC impedance?

• A. Z = R - j(ωL - 1/(ωC))
• B. Z = R + j(ωC - 1/(ωL))
• C. Z = R + j(ωL - 1/(ωC))
• D. Z = R + j(ωL - 1/(ωC))

Answer: (D)

In a series RLC circuit, impedances add. The inductor contributes ZL = jωL and the capacitor contributes ZC = 1/(jωC) = -j/(ωC). Adding them with the resistor gives Z = R + jωL - j/(ωC) = R + j(ωL - 1/(ωC)). The reactive part is the imaginary term, j(ωL - 1/(ωC)). So the correct description of the reactive component is Z = R + j(ωL - 1/(ωC)); the sign and the combination show how the inductive and capacitive effects compete. If ωL is larger, the circuit behaves inductively; if 1/(ωC) is larger, it’s more capacitive.

In a series RLC circuit, impedances add. The inductor contributes ZL = jωL and the capacitor contributes ZC = 1/(jωC) = -j/(ωC). Adding them with the resistor gives Z = R + jωL - j/(ωC) = R + j(ωL - 1/(ωC)). The reactive part is the imaginary term, j(ωL - 1/(ωC)). So the correct description of the reactive component is Z = R + j(ωL - 1/(ωC)); the sign and the combination show how the inductive and capacitive effects compete. If ωL is larger, the circuit behaves inductively; if 1/(ωC) is larger, it’s more capacitive.