Generators · Grade 12
In Grade 12 you learn: peak e.m.f. ε₀ = NBAω.
Moving a wire across a magnetic field, or changing the field through a coil, induces a voltage: the generator effect. A generator spins a coil in a magnetic field, so kinetic energy becomes electrical energy. An alternator gives alternating current through slip rings; a dynamo gives direct current through a commutator. Spinning faster gives a bigger, more frequent output.
Key facts
- An alternator uses slip rings and gives a.c.; a dynamo uses a commutator and gives d.c.
- Spinning a generator faster raises both the peak e.m.f. and the frequency.
- Peak e.m.f. ε₀ = NBAω, with ω = 2πf. Frequency (Hz) = revolutions per minute ÷ 60.
Worked examples
Example 1
What is the difference between an alternator and a dynamo?
Answer: An alternator uses slip rings and gives a.c.; a dynamo uses a split-ring commutator and gives d.c.
Example 2
The trace shows two cycles of a generator’s output taking 40 ms, with a peak of 12 V. Find the period and frequency.
Answer: T = 20 ms, f = 50 Hz
Example 3
A generator gives a peak of 8 V at 25 Hz. What happens if it spins three times as fast?
Answer: peak 24 V, frequency 75 Hz
Example 4
A generator coil turns at 1,200 revolutions per minute. What is the frequency of its a.c. output, and hence its period in ms? Give the period.
Answer: 50 ms
Example 5
In a generator, when is the induced e.m.f. largest?
Answer: when the coil’s plane is parallel to the field (cutting field lines fastest)
Example 6
A generator coil has 90 turns of area 136 cm² and spins at 50 revolutions per second in a 0.3 T field. Find the peak e.m.f., to 3 significant figures. (ε₀ = NBAω, ω = 2πf)
Answer: 115 V