| TAP 416-3: Alternating current generators
Thinking about generators and induced emf
An emf is induced in a coil when the magnetic flux through the coil changes. The emf in volts is numerically equal to the rate of change of flux linked, in Weber turns per second. Use these principles to answer the following questions.
A cycle dynamo
A cycle dynamo has a permanent magnet that spins inside a cylindrical stator made of iron. On the inside of the stator there are pole pieces wound with coils.
1. As the magnet turns, when is the flux through the coils greatest? When is it least?
2. The magnet rotates 10 times a second. In approximately what time does the flux through the coils go from its least value to its largest value?
3. At this speed the dynamo produces an alternating emf just enough to light a lamp, and so of the order of magnitude 2 V. Estimate the largest flux through the coils, if the coils have 500 turns in all.
4. If the coils have cross section of 20 mm 20 mm estimate the flux density in the coils when the flux is a maximum
Spinning a coil in a magnet
A large Alnico horseshoe magnet produces a uniform flux density of 0.5 T between its poles. The poles have a cross section of 50 mm 20 mm.
5. Estimate the flux between the pole pieces.
6. A circular search coil of radius 10 mm is placed between the poles. How must it be placed so as to have the maximum flux through it? Estimate that maximum flux.
7. The search coil is rotated through 180, in a time of 1/10 s. Estimate the magnitude of the emf that would be detected briefly across each turn of the coil.
8. The search coil has 500 turns. What emf is expected across the coil in the conditions of question 7?
9. If the coil is rotated continually like this, how does the emf across it vary?
A large alternator
A large alternating current generator (alternator) is to be designed. It is to produce an alternating emf of maximum value 10 kV at a frequency of 50 Hz. The design has a cylindrical stator with fixed coils in which the induced emf is generated. The emf is generated by rotating a cylindrical ac electromagnet rotor inside the stator, at 50 rotations per second.
10. Calculate the maximum rate of change of flux linkage through the stator coils, in Weber turns per second.
11. If the emf and flux are varying sinusoidally at frequency f, the maximum rate of change of flux is 2f times the maximum value of the flux. Calculate the maximum flux linkage through the coils of the stator.
12. The stator coils are wound with 300 turns. What is the magnetic flux through them, in Webers?
13. The largest flux density that can be achieved in the air gap between rotor and stator is 0.1 T. What must be the design area of the stator coils?
These questions provide practice in calculating rates of change of flux and flux linkage, and emf. The most likely source of difficulty will be distinguishing between flux F and flux linkage N F, and remembering which of them is in use at a given point in the calculation. It may be worth stressing that the rate of change of magnetic flux gives the emf per turn.
Social and human context
High-powered generators have to be very big. You may have seen one being transported slowly by road on a long trailer with police escort.
Answers and worked solutions
1. The flux is greatest when the magnet is lined up with the pole pieces. The flux is least when the magnet is at right angles to the pole pieces.
2. Approximately 1/4 rotation, so 1/4 1/10 s = 1/40 s.
3. Emf = flux change turns / time. Flux change = emf time / turns:
4. Area of coils = 20 mm 20 mm = 400 mm2 = 4 10–4 m2. Bfield = flux / area:
5. Flux = flux density area. Area = 20 mm 50 mm = 1000 mm2 = 10–3 m2:
6. Centre the coil between the pole pieces, with its plane parallel to the pole pieces:
7. emf time = change of flux. The flux reverses so the change of flux is 3 10–4 Wb:
8. With 500 turns emf = 3 mV per turn 500 turns = 1.5 V.
9. The emf alternates sinusoidally.
10. emf = rate of change of flux linkage = 104 Wb turns per second.
11. Maximum flux = maximum flux linkage / 2f:
12. Flux = flux linkage / turns:
This activity is taken from Advancing Physics chapter 15, 180S