Electro-Magnetic Induction © D Hoult 2008

The Transformer

weak induced alternating emf

iron core

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

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)

The Ideal Transformer Therefore, in an ideal transformer:

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

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

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

The Ideal Transformer

The Ideal Transformer When Ip changes, f changes.

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

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

At the primary coil, the magnitude of the induced emf is given by Df Ep = - Np Dt

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

Ep Np = Es Ns

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

The power input to the primary coil is given by

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

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 =

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

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

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

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.

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”.