AC Generator
ε(t) = NBAω sin(ωt). Rotating coil between magnetic poles.
Key Notes
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.
Formulas
Instantaneous EMF
Coil rotates about an axis perpendicular to B.
Peak EMF
Linear in N, B, A, and ω.
Flux variation
Sinusoidal — gives EMF via Faraday.
Frequency
For an N-pole machine; 2-pole at 3000 rpm gives 50 Hz.
Important Points
EMF is purely sinusoidal because the projection of the area vector onto B varies as cos(ωt).
Doubling rotation speed DOUBLES both frequency AND peak EMF (ε₀ = NBAω contains ω).
Hydro generators run slow (~100 rpm) with many magnetic poles to get 50 Hz; steam turbines run fast (~3000 rpm) with 2 poles.
Real generators have armature reaction (induced fields modify the main B) and core losses — neglected at this level.
Slip rings → AC output. Commutator → DC output. Same coil, different terminal scheme.
Energy comes from MECHANICAL work done against the Lenz-law force on the rotating coil — no free energy.
AC Generator notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.