Faraday's law states that a changing magnetic flux through a circuit induces an EMF equal in magnitude to the rate of flux change and directed (by Lenz's law) to oppose that change.

The negative sign in EMF = −dΦ/dt is Lenz's law: the induced current fights the cause that produced it, ensuring energy is conserved (work must be done to change the flux).

Motional EMF arises because the Lorentz force qv × B separates charges in a moving conductor, creating a potential difference ε = Bvl when v, B, and l are mutually perpendicular.

A coil rotating in a magnetic field generates sinusoidal AC output with peak EMF ε_{0} = NBAω, which is the operating principle of all AC generators.

Self-inductance L (henry) is the property of a coil that opposes changes in its own current through a back-EMF ε = −L(dI/dt), and stores energy U = ½$LI^{2}$ in its magnetic field.

In AC circuits, inductors oppose current proportional to frequency (X_L = ωL), while capacitors pass current more easily at higher frequencies (X_C = 1/ωC).

The mnemonic ELI the ICE man captures all phase relationships: in an inductor voltage leads current; in a capacitor current leads voltage.

In a series LCR circuit, resonance occurs when X_L = X_C, giving minimum impedance Z = R (not zero), maximum current, and unity power factor.

The transformer changes AC voltage levels using mutual inductance: voltage and turns ratio are directly proportional, while the current ratio is inversely proportional.

High-voltage power transmission exploits transformers to reduce current and thereby minimize $I^{2}$R losses over long distances, making the electrical grid economically feasible.