Impedans

Impedans, or impedance, is the opposition that a circuit presents to alternating current and time-varying signals. It is a complex quantity denoted Z, with a real part called resistance R and an imaginary part called reactance X. In mathematical form: Z = R + jX, where j is the imaginary unit. The magnitude is |Z| = sqrt(R^2 + X^2) and the phase angle is φ = arctan(X/R). Reactance depends on frequency: inductive reactance X_L = ωL and capacitive reactance X_C = -1/(ωC). Consequently, Z for a resistor is R, for a capacitor is 1/(jωC) = -j/(ωC), and for an inductor is jωL.

In circuits, impedances add according to connections: in series, Z_total = Z1 + Z2 + ...; in parallel, 1/Z_total = 1/Z1 + 1/Z2 + ... This enables analysis of AC circuits with phasors and complex algebra.

Impedance is central to impedance matching, which aims to maximize power transfer or minimize reflections by choosing source and load impedances that are complex conjugates.

Measurement and applications: Impedance can vary with frequency due to material properties or device dynamics. Impedance spectroscopy studies this dependence to characterize components, materials, or electrochemical cells, often using Nyquist or Bode representations. Practical uses appear in audio electronics, transmission lines, sensors, and medical instrumentation.