AC generator and transformer
AC generator (dynamo): converts mechanical energy into electrical energy using electromagnetic induction. A coil of N turns and area A rotates with angular speed ω in a uniform field B. The flux through it is Φ = BA cos ωt, so the induced emf is ε = NBAω sin ωt, with peak emf ε₀ = NBAω. The emf is maximum when the plane of the coil is parallel to B (flux zero but changing fastest) and zero when the plane is perpendicular to B. The main parts are the armature coil, field magnets, slip rings and carbon brushes.
Worked example: N = 100, B = 0.1 T, A = 0.02 m², rotating at 50 rev/s (ω = 100π rad/s). ε₀ = 100 × 0.1 × 0.02 × 100π ≈ 62.8 V.
Transformer: changes the size of an alternating voltage using mutual induction. Two coils (primary and secondary) are wound on a laminated soft-iron core. For an ideal transformer: V_s/V_p = N_s/N_p = I_p/I_s.
- Step-up: N_s > N_p, voltage increases, current decreases.
- Step-down: N_s < N_p, voltage decreases, current increases.
Power in = power out (ideal): V_p I_p = V_s I_s. A transformer does not work with steady DC because the flux would not change.
Energy losses in real transformers:
- Flux leakage (reduced by winding coils over each other).
- Copper loss, I²R heating of windings (thick wires).
- Eddy-current loss in the core (laminated core).
- Hysteresis loss (soft-iron core with low hysteresis).
Key points
- ε₀ = NBAω for a generator.
- V_s/V_p = N_s/N_p; ideal: V_pI_p = V_sI_s.
- Transformers work only with AC.
- Step-up increases voltage but decreases current; power is not increased.
Exam tips
- Transformer ratio problems are quick: set up V_s/V_p = N_s/N_p.
- Remember that frequency stays the same in a transformer.
Common mistakes
- Thinking a step-up transformer increases power or energy.
- Applying the turns ratio to current the same way as to voltage (it is inverted).
- Believing a transformer works on DC.