AC Generators (HL) (HL IB Physics)

• If a coil of wire is rotated inside a magnetic field by an external force, an emf will be generated in the wire which causes current to flow within the coil
• The generator effect can be used to:
  • Generate a.c. in an alternator
  • Generate d.c. in a dynamo

Alternators

• A simple alternator is a type of generator that converts mechanical energy to electrical energy in the form of alternating current

An alternator is a rotating coil in a magnetic field connected to commutator rings

• A rectangular coil that is forced to spin in a uniform magnetic field
• The coil is connected to a centre-reading meter by metal brushes that press on two metal slip rings (or commutator rings)
  • The slip rings and brushes provide a continuous connection between the coil and the meter

• When the coil turns in one direction:
  • The pointer defects first one way, then the opposite way, and then back again
  • This is because the coil cuts through the magnetic field lines and a potential difference, and therefore current, is induced in the coil

• The pointer deflects in both directions because the current in the circuit repeatedly changes direction as the coil spins
  • This is because the induced potential difference in the coil repeatedly changes its direction
  • This continues on as long as the coil keeps turning in the same direction

• The induced potential difference and the current alternate because they repeatedly change direction

An example current output from an alternator

Dynamos

• A dynamo is a direct-current generator
• A simple dynamo is the same as an alternator except that the dynamo has a split-ring commutator instead of two separate slip rings

A dynamo is a rotating coil in a magnetic field connected to a split ring commutator

• As the coil rotates, it cuts through the field lines
  • This induces a potential difference between the end of the coil
• The split ring commutator changes the connections between the coil and the brushes every half turn in order to keep the current leaving the dynamo in the same direction
  • This happens each time the coil is perpendicular to the magnetic field lines

  

  D.C output from a dynamo - the current is only in the positive region of the graph

• Therefore, the induced potential difference does not reverse its direction as it does in the alternator
• Instead, it varies from zero to a maximum value twice each cycle of rotation, and never changes polarity (positive to negative)
  • This means the current is always positive (or always negative)

• When a coil rotates in a uniform magnetic field, the flux through the coil will vary as it rotates
• Since e.m.f is the rate of change of flux linkage, this means the e.m.f will also change as it rotates 
  • The maximum e.m.f is when the coil cuts through the most field lines
  • The e.m.f induced is an alternating voltage

• Flux linkage is given by

• Angular speed ω is defined as the rate of change of angular displacement, so

• Therefore, for a rotating coil, the angle θ depends on the angular speed of the coil ω:

• Hence, flux linkage can also be written as:

• Where:
  • = flux linkage (Wb turns)
  • B = magnetic flux density (T)
  • A = cross-sectional area of the coil (m²)
  • N = number of turns of coil
  • ω = angular speed of the coil (rad s^-1)
  • t = time (s)

Flux linkage and induced e.m.f. in a rotating coil

• The graph shows that
  • The induced e.m.f varies sinusoidally and it is 90° out of phase with the flux linkage

• Mathematically, the induced e.m.f. can also be written as:

• Where:
  • ε = e.m.f induced in the coil (V)
  • ε₀ = maximum e.m.f induced in the coil (V)

• The size of the induced e.m.f. in a rotating coil can be increased by increasing the frequency of rotation of the coil
• Increasing the coil's frequency of rotation increases:
  • The frequency of the alternating voltage
  • The amplitude of the alternating voltage

Doubling the angular speed of the rotating coil in a magnetic field doubles the size of the induced e.m.f. (double the amplitude) and the frequency of the rotation (half the time period)