Syllabus Edition

First teaching 2023

First exams 2025

|

AC Generators (HL) (HL IB Physics)

Revision Note

Katie M

Author

Katie M

Last updated

The AC generator

  • If a coil of wire is rotated inside a magnetic field by an external force, an e.m.f. will be generated in the wire which causes current to flow within the coil
  • A simple A.C. generator converts mechanical energy into electrical energy in the form of alternating current

Alternator, downloadable IGCSE & GCSE Physics revision notes

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

  • A rectangular coil 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 as long as the coil keeps turning in the same direction
  • The induced potential difference and the current alternate because they repeatedly change direction

a-c--generator-graphs-01

As the coil rotates in the magnetic field, the changing magnetic flux causes the induction of e.m.f. in the opposite sides of the coil

Emf Induction in a Rotating Coil

  • 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

N capital phi space equals space B A N space cos space theta

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

omega space equals space theta over t

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

theta space equals space omega t

  • Hence, flux linkage can also be written as:

N capital phi space equals space B A N space cos space omega t

  • Where:
    • N capital phi = 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)

4-4-5-induced-emf-in-a-rotating-coil

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:

epsilon space equals space epsilon subscript 0 space sin space omega t

epsilon space equals space B A N omega space sin space omega t

  • 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

4-4-5-induced-emf-in-a-rotating-coil-effect-of-angular-velocity

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)

Worked example

An alternating current generator induces an e.m.f. of epsilon at a frequency f.

The rotational speed of the coil in the generator is doubled.

Which row correctly identifies the new output e.m.f. and the new frequency?

  e.m.f. frequency
 A. 2 epsilon 2 f
 B. square root of 2 epsilon 2 f
 C. 2 epsilon f over 2
 D. square root of 2 epsilon f over 2

Answer:  A

  • Angular speed, time period and frequency are related by

omega space equals space fraction numerator 2 straight pi over denominator T end fraction space equals space 2 straight pi f

  • Therefore, omega space proportional to space f, so if angular speed doubles, the frequency will also double
  • If the coil rotates at twice the frequency, the rate of change of magnetic flux linkage will double
  • Hence, induced e.m.f. and angular speed are directly proportional epsilon space proportional to space omega
  • This means the induced e.m.f. will double if angular speed doubles

new e.m.f. = 2 epsilon, new frequency = 2 f

Examiner Tip

Remember not to get mixed up with when the e.m.f or the flux linkage is at its maximum:

  • When the plane of the coil is perpendicular to the field lines
    • The flux linkage is at its maximum
    • The e.m.f = zero
  • When the plane of the coil is parallel to the field lines
    • The flux linkage is zero 
    • The e.m.f is at its maximum

Since ω is in units of rads s-1, make sure your calculator is in radians mode before entering any values into sin(ωt) or cos(ωt).

The equation of e.m.f with sin(ωt) is not given in your data booklet - you must be able to recognise this in exam questions!

You've read 0 of your 10 free revision notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.