Define impedance for a resistor-inductor-capacitor circuit.

Define impedance for a resistor-inductor-capacitor circuit.

• A. Z = R + jX
• B. Z = R - jX
• C. Z = R × jX
• D. Z = 1/(R + jX)

Answer: (A)

In AC circuits, impedance combines resistance and reactance into a complex quantity: Z = R + jX. Here, R is the resistive part that dissipates real power, and X is the net reactance from the inductor and capacitor, X = X_L − X_C = ωL − 1/(ωC). For a resistor–inductor–capacitor network, this gives Z = R + j(ωL − 1/(ωC)). The plus sign with j allows X to be positive (net inductive) or negative (net capacitive), so the standard form is Z = R + jX. The other forms don’t match how impedance mounts the real and imaginary parts. Z = R − jX would just be a redefinition of X as negative, not the conventional expression. Z = R × jX mixes the quantities in a non-physical way for impedance, and Z = 1/(R + jX) is the reciprocal, which would relate to admittance rather than impedance.

In AC circuits, impedance combines resistance and reactance into a complex quantity: Z = R + jX. Here, R is the resistive part that dissipates real power, and X is the net reactance from the inductor and capacitor, X = X_L − X_C = ωL − 1/(ωC). For a resistor–inductor–capacitor network, this gives Z = R + j(ωL − 1/(ωC)). The plus sign with j allows X to be positive (net inductive) or negative (net capacitive), so the standard form is Z = R + jX.

The other forms don’t match how impedance mounts the real and imaginary parts. Z = R − jX would just be a redefinition of X as negative, not the conventional expression. Z = R × jX mixes the quantities in a non-physical way for impedance, and Z = 1/(R + jX) is the reciprocal, which would relate to admittance rather than impedance.