AC & the Generator
A spinning coil makes alternating emf.
Lesson at a glanceShow the key points
- AC: i = i₀ sin(ωt + φ) (39.1), period 2π/ω.
- Generator: magnet, armature on slip rings, brushes.
- ℰ = NBAω sin ωt (39.2); peak NBAω.
The electricity in your walls doesn’t flow one way: it surges back and forth fifty or sixty times a second. That alternating current comes straight from Faraday’s law applied to a spinning coil.
Alternating current
A battery drives current one way at a nearly steady size. A current whose direction keeps reversing is an alternating current (AC). We study the sinusoidal kind:
The current is positive for half of each period and negative for the other half. To drive it we need a source of sinusoidal emf: an AC generator (AC dynamo), which turns mechanical energy into electrical energy.
How a generator works
- Magnet: permanent or electro-, with facing poles giving a strong uniform field B.
- Armature: a coil, usually on a soft-iron core to strengthen the field, turning about an axis in its own plane and perpendicular to B. Its ends go to two slip rings.
- Brushes: two graphite brushes press on the rings and connect to the outer terminals, keeping contact as the rings turn.
Let the coil (N turns, area A) turn at constant ω, with its plane perpendicular to B at t = 0. The flux through each turn is BA cos ωt, so each turn has emf −dΦ/dt = BAω sin ωt, and the whole coil:
A 100-turn coil of area 200 cm² spins at 50 revolutions per second in a 0.25 T field. Find its peak emf.
- 1AC reverses direction periodically: i = i₀ sin(ωt + φ) (39.1).
- 2Generator: magnet, armature on slip rings, brushes.
- 3A coil spinning in B gives ℰ = NBAω sin ωt (39.2).
Check yourself
Keep exploring
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