The impedance Z of a series RLC circuit in phasor form is given by which of the following?

• 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(1/(ωL) - ωC)

Answer: (C)

In a series RLC circuit, impedances simply add: Z = Z_R + Z_L + Z_C. The resistor contributes R (real), the inductor contributes jωL (positive imaginary), and the capacitor contributes -j/(ωC) (negative imaginary). Adding them gives Z = R + jωL - j/(ωC) = R + j(ωL − 1/(ωC)). This matches the given correct form. The imaginary part, ωL − 1/(ωC), tells you whether the net reactance is inductive (positive) or capacitive (negative) at the operating frequency. The other expressions misplace signs or terms and do not correspond to the standard impedances of the inductor or capacitor in a series configuration.