voltageimpedance

Voltage impedance is the characteristic that determines how a circuit or component resists the flow of alternating current in response to an applied voltage. In linear, time-invariant circuits, impedance Z is defined as the complex ratio of the phasor voltage V to the phasor current I, Z = V/I. Impedance is a complex quantity Z = R + jX, where R is the resistive part and X is the reactive part. The reactive part accounts for energy storage in magnetic (inductive) or electric (capacitive) fields.

For an inductor, Z_L = jωL; for a capacitor, Z_C = 1/(jωC) = -j/(ωC). At DC (ω = 0), capacitive impedance tends to infinity and inductive impedance tends to zero, leaving only resistance. In AC circuits, impedance generalizes Ohm's law: V = IZ. The magnitude |Z| indicates how much the current is reduced for a given voltage, while the phase angle φ = arg(Z) describes the lead/lag between voltage and current. The real part P = VI cosφ is the average power, and Q = VI sinφ is the reactive power; apparent power S = VI.

Impedance combines in series and parallel like resistances, with Z_total = Z1 + Z2 for series, and 1/Z_total = 1/Z1 + 1/Z2 for parallel. Admittance Y = 1/Z is useful for parallel combinations. Applications include impedance matching in RF, filter design, and circuit analysis. Measurement of impedance is performed with LCR meters or impedance analyzers.