Generators

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

  • The generator effect: moving a wire or coil through a magnetic field, or moving a magnet in a coil, induces a voltage.
  • Motor: electrical → kinetic energy. Generator: kinetic → electrical energy.
  • 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 energy transfer happens in a generator?

  1. Something has to turn a generator: it is given kinetic energy.
  2. Turning the coil in a magnetic field induces a voltage.
  3. So kinetic energy is transferred to electrical energy.

Answer: kinetic → electrical

Example 2

A magnet is pushed into a coil joined to a sensitive ammeter, and the needle flicks to the right. What happens when the magnet is pulled out again?

  1. Moving the magnet changes the magnetic field through the coil, which induces a voltage and a current.
  2. Moving it the other way induces a current the other way, so the needle flicks the other way.
  3. If the magnet is held still, nothing is induced.

Answer: The needle flicks to the left: the induced current reverses.

Example 3

How can you make a generator give a bigger voltage?

  1. The induced voltage depends on how fast the magnetic field through the coil changes.
  2. Spinning faster, more turns of wire and a stronger magnet all make it change faster, so the voltage is bigger.

Answer: Spin it faster, use more turns on the coil, or use a stronger magnet.

Example 4

In a moving-coil microphone, what happens when sound hits the diaphragm?

  1. Sound makes the diaphragm, and the coil fixed to it, vibrate.
  2. The coil moves in a magnetic field.
  3. This induces a voltage in the coil (generator effect).

Answer: The coil moves in a magnetic field and a voltage is induced

Example 5

What is the difference between an alternator and a dynamo?

  1. An alternator uses slip rings: each end of the coil stays on the same brush, so the output alternates (a.c.).
  2. A dynamo uses a split-ring commutator, which swaps the connections every half turn.
  3. So a dynamo’s output always flows one way (d.c.).

Answer: An alternator uses slip rings and gives a.c.; a dynamo uses a split-ring commutator and gives d.c.

Example 6

The trace shows two cycles of a generator’s output taking 40 ms, with a peak of 12 V. Find the period and frequency.

  1. Two cycles take 40 ms, so one takes half. 40 ms ÷ 2 = 20 ms
  2. Frequency = 1 ÷ period. f = 1 ÷ 0.020 = 50 Hz

Answer: T = 20 ms, f = 50 Hz

Example 7

A generator gives a peak of 8 V at 25 Hz. What happens if it spins three times as fast?

  1. The flux changes three times as fast, so the peak is 3 times bigger. 8 × 3 = 24 V
  2. It also makes three times as many cycles each second. 25 × 3 = 75 Hz

Answer: peak 24 V, frequency 75 Hz

Example 8

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.

  1. One revolution gives one cycle, so f = revolutions per second.
  2. f = 1,200 ÷ 60 = 20 Hz
  3. T = 1 ÷ 20 = 0.05 s = 50 ms

Answer: 50 ms

Example 9

In a generator, when is the induced e.m.f. largest?

  1. The induced e.m.f. depends on how fast the flux changes.
  2. When the coil’s plane is parallel to the field, its sides move straight across the field lines.
  3. They cut field lines fastest, so the e.m.f. is largest.

Answer: when the coil’s plane is parallel to the field (cutting field lines fastest)

Example 10

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)

  1. Change the area to m²: 136 cm² = 0.0136 m².
  2. ω = 2π × 50 = 314.16 rad/s
  3. ε₀ = 90 × 0.3 × 0.0136 × 314.16 = 115.4 V

Answer: 115 V