Impedance

A circuit or components impedance is how much it opposes an alternating current. It is roughly analogous to resistance in a D/C circuit. Impedance is the ratio of voltage amplitude to current amplitude:

These next examples assume an A/C circuit where the driving voltage is $V(t) = V_0 \sin(\omega t)$ and the current is $I(t) = I_0 \sin(\omega t - \phi)$.

Resistor

In an A/C circuit, a resistor simply has impedance $Z_R = R$ since the current through it is related to voltage by $V=IR$.

Inductor

In an A/C circuit, an inductor has impedance $Z_L = \omega L$ where $\omega$ is the driving frequency of the circuit (the frequency of the voltage). This is because voltage and current through an inductor are related by $V = L \frac{dI}{dt}$ and differentiating current gives an $\omega$ term.

Capacitor

In an A/C circuit, a capacitor has impedance $Z_C = \frac{1}{\omega C}$ where $\omega$ is the driving frequency. The equation for a capacitor is $Q=CV$ and we differentiate both sides to relate voltage and current. This gives a $\omega C$ on the voltage side of the equation (from differentiating).