AC Generator

An AC generator converts mechanical rotation into electrical AC by spinning a coil in a uniform magnetic field.

EMF: ε(t) = N·B·A·ω·sin(ωt), where N = turns, B = field, A = coil area, ω = angular speed.

Peak EMF: ε₀ = NBAω. Frequency f = ω/(2π) — directly set by rotation rate.

Flux through the coil: Φ = NBA·cos(ωt). The EMF is −dΦ/dt = NBAω·sin(ωt) — exactly Faraday's law.

Slip rings and brushes feed AC out (without rectification). A commutator (split-ring) would convert it to DC.

Most power plants — thermal, hydro, nuclear, wind — drive a turbine that turns a 3-phase generator. The grid runs at fixed f (50 Hz in India, 60 Hz in US).

Indian power-plant generators run typically at 3000 rpm to produce 50 Hz from a 2-pole machine.