Explain the principle and working of an AC generator with a labelled diagram. Derive the expression for the instantaneous emf induced.

1. 1 · State the principle. Electromagnetic induction: a coil rotating in a magnetic field has a changing flux linkage.
2. 2 · Draw the diagram. [Magnet poles N and S; coil ABCD on an axle; slip rings R₁ and R₂; brushes B₁ and B₂; external load; rotation arrow]
3. 3 · Describe the working. A turbine turns the coil; the slip rings and brushes take the alternating current to the load.
4. 4 · Write the flux. At time t, θ = ωt, so NΦ = NBA cos ωt.
5. 5 · Derive the emf. ε = −N dΦ/dt = NBAω sin ωt = ε₀ sin ωt, with ε₀ = NBAω.
6. 6 · Describe the output. The emf reverses every half rotation, so the output is AC of frequency ν = ω/2π.
7. 7 · Real life. Power stations and diesel generator sets work this way.
8. 8 · Close in one line. So, mechanical energy is changed into electrical energy by electromagnetic induction.

Scoring tip: Label the slip rings and brushes in the diagram; that is where most students lose marks.