Transformers

AC generators in power stations use electromagnetic induction to convert kinetic into electrical energy. Electromagnetic induction is then used in transformers to transmit the electricity efficiently to where it is needed.


Key Concepts

Operation

A transformer consists of two coils - primary and secondary. The primary coil produces a changing magnetic field due to the alternating current supplied within. The secondary coil cuts the changing magnetic flux and a changing EMF is induced, causing a current to flow. The strength of the magnetic field is increased by the presence of the solf iron core.

Equation

A step-up transformer increases the EMF and has more turns on the secondary coil in comparison with the primary. A step-down transformer decreases EMF and has a reduction in the number of turns.

In both cases, the ratio of the EMFs is equal to the ratio of the turns:

\({\varepsilon_p\over \varepsilon_s}={N_p\over N_s}\)

If the transformer is ideal, the power input is equal to the power output:

\(I_p\varepsilon_p=I_s\varepsilon_s\)

\(\Rightarrow {\varepsilon_p\over \varepsilon_s}={N_p\over N_s}={I_s\over I_p}\)

  • \(\varepsilon_p\) is the EMF on the primary coil (V)
  • \(\varepsilon_s\) is the EMF on the secondary coil (V)
  • \(N_p\) is the number of turns on the primary coil
  • \(N_s\) is the number of turns on the secondary coil
  • \(I_s\) is the current in the secondary coil (A)
  • \(I_p\) is the current in the primary coil (A)

Essentials

Power transmission

The process of transmitting electrical power from a generator to a town is optimised to reduce thermal energy losses.

The main culprit is usually thermal energy loss in power lines, due to the size of the current. To reduce this current and hence the wasted energy:

  1. A step-up transformer is used before the power lines (to increase voltage an reduce current)
  2. A step-down transformer is used after the power lines (to reduce voltage to an acceptable size for household use)

Non-ideal transformers

There are several reasons why transformers are not ideal:

  • Flux leakage - some of the flux does not travel through the soft iron core but instead through the air. This is not cut by the secondary coil.
  • Joule heating - the currents in the coils will experience resistance and release thermal energy
  • Eddy current heating - the soft iron core will be subject to the induction of loops of current perpendicular to the field. These will release thermal energy.
  • Magnetic hysteresis - when a magnetic field is applied to the soft iron core, the atomic domains align themselves with it. Even when the field is removed, part of the alignment will be retained: the material has become magnetized. This alignment requires work to be overcome as the field direction changes continuously.

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