A coil turning in a field.

• 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.

Teaching this idea? Put the simulation on your own page or LMS with this code.