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Impedance Z = R + jX extends Ohm's law to AC circuits: V̅ = Z I̅. The real part R is resistance; the imaginary part X is reactance (inductive or capacitive). Series impedances add; parallel admittances (Y = 1/Z) add. This allows AC circuits to be analyzed using the same techniques as DC circuits, but in the complex plane.
You know how to analyze DC circuits using Ohm's law (V = IR) and Kirchhoff's laws. You also know from phasor representation that sinusoidal voltages and currents can be written as complex numbers that encode both amplitude and phase. Impedance unifies these two ideas: it extends Ohm's law to AC circuits by treating all three passive elements through a single complex quantity Z, so that V̅ = Z·I̅ works in the phasor domain exactly as V = IR works in DC.
Each element type has a characteristic impedance. A resistor has Z_R = R — purely real, no phase shift, just as in DC. A capacitor has Z_C = 1/(jωC), which is purely imaginary and negative; current leads voltage by 90°. An inductor has Z_L = jωL, purely imaginary and positive; voltage leads current by 90°. The imaginary part X is called reactance: capacitive (X_C = −1/ωC) and inductive (X_L = ωL). The full impedance Z = R + jX captures both the resistive and reactive character of a network.
The combination rules carry over from DC without modification — just use complex arithmetic. Series impedances add: Z_total = Z₁ + Z₂ + ··· For parallel combinations, it's often easier to work with admittance Y = 1/Z (the AC generalization of conductance). Parallel admittances add: Y_total = Y₁ + Y₂ + ···, then Z_total = 1/Y_total. Voltage divider and current divider rules are identical to DC — replace R with Z throughout. This is the payoff of phasor analysis: an AC circuit with any mix of R, L, C elements becomes a DC-style resistor network in the complex domain.
The magnitude |Z| gives the ratio of voltage amplitude to current amplitude; the angle ∠Z gives the phase difference. For Z = 3 + 4j Ω, the magnitude is 5 Ω and the phase is arctan(4/3) ≈ 53°, meaning voltage leads current by 53°. This single complex number encodes the full sinusoidal relationship between V and I. Everything in AC circuit analysis — resonance, filters, power factor, Thevenin equivalents — begins with impedance as the fundamental building block.