AC generator

An ac generator turns mechanical energy into electrical energy by rotating a coil in a magnetic field, which changes the angle θ between B and the coil's area vector.

Its parts: a coil (the armature) on a rotor shaft whose axis is at right angles to B, turned by some outside means. The coil's ends connect to the outside circuit through slip rings and brushes.

Turning at steady angular speed ω with θ = ωt, the flux through N turns is NBA cos ωt, so ε = NBAω sin ωt = ε₀ sin ωt, with peak ε₀ = NBAω.

The emf is largest when θ = 90° or 270°, where the coil's plane lies along B and the flux, though zero, is changing fastest. It is zero when the plane faces the field and the flux is largest.

The polarity reverses every half turn, so the current is alternating (ac). With ω = 2πν, ε = ε₀ sin 2πνt, where ν is the rotation frequency.

Commercial generators are turned by falling water (hydro-electric), by steam raised with coal or other fuel (thermal), or by steam from nuclear fuel. A typical large machine gives about 100 MW, and some give 500 MW. Usually the coils are fixed and electromagnets rotate.

The supply frequency is 50 Hz in India and 60 Hz in some countries such as the USA.

Example 6.10: a 100-turn coil of area 0.10 m² turned at 0.5 rev/s in 0.01 T gives ε₀ = 100 × 0.01 × 0.1 × 2π × 0.5 = 0.314 V.