1. Electro-Magnetic Induction
© D Hoult 2008

2. The Transformer

8. weak induced alternating emf

9. iron core

12. The Ideal Transformer
If a transformer is described as ideal we mean it is 100% efficient

13. The Ideal Transformer
If a transformer is described as ideal we mean it is 100% efficient
In other words, power output (at secondary coil) equals power input (to primary coil)

14. The Ideal Transformer
Therefore, in an ideal transformer:

15. The Ideal Transformer
Therefore, in an ideal transformer:
i) the coils have zero resistance

16. The Ideal Transformer
Therefore, in an ideal transformer:
i) the coils have zero resistance
ii) all the magnetic flux f produced by the primary current Ip is linked with the secondary coil

17. The Ideal Transformer
Therefore, in an ideal transformer:
i) the coils have zero resistance
ii) all the magnetic flux f produced by the primary current Ip is linked with the secondary coil
iii) no current flows in the iron core

18. The Ideal Transformer

19. The Ideal Transformer
When Ip changes, f changes.

20. The Ideal Transformer
When Ip changes, f changes.
When f changes, an emf is induced in both coils.

21. At the primary coil, the magnitude of the induced emf is given by

22. At the primary coil, the magnitude of the induced emf is given byDf
Ep = - Np Dt

23. At the primary coil, the magnitude of the induced emf is given byDf
Ep = - Np Dt
as we are assuming zero resistance coils, the supply voltage must also have this magnitude in order to maintain the flow of current

24. At the primary coil, the induced emf is given byDf
Ep = - Np Dt
as we are assuming zero resistance coils, the supply voltage must also have this magnitude in order to maintain the flow of current
At the secondary coil, the magnitude of the induced emf is given by Df
Es = - Ns Dt

25. Ep Np = Es Ns

26. Ep Np = Es Ns
here we are assuming that f is the same for both coils

27. The power input to the primary coil is given by

28. The power input to the primary coil is given by
power in = Ep Ip

29. The power input to the primary coil is given by
power in = Ep Ip
The power output from the secondary coil is given by
power out =

30. The power input to the primary coil is given by
power in = Ep Ip
The power output from the secondary coil is given by
power out = Es Is

31. The power input to the primary coil is given by
power in = Ep Ip
The power output from the secondary coil is given by
power out = Es Is
as we are considering an ideal transformer

32. The power input to the primary coil is given by
power in = Ep Ip
The power output from the secondary coil is given by
power out = Es Is
as we are considering an ideal transformer
Ep Ip = Es Is

33. Ep Ip = Es Is
Therefore, with an ideal transformer, when the secondary coil is open circuit (not connected to anything), there is no net energy taken from the supply.

34. Ep Ip = Es Is
Therefore, with an ideal transformer, when the secondary coil is open circuit (not connected to anything), there is no net energy taken from the supply.
Energy is stored in the magnetic field during the time the current is increasing but is recovered from the field when it “collapses”.