An Ideal Transformer


An Ideal Transformer

An ideal transformer is one which has no ohmic resistance and no magnetic leakage flux i.e. all the flux produced in the core links with primary as well as secondary winding. In other words, we are postulating the following:

  • The core of the transformer is highly permeable in a sense that it requires vanishingly small magnetomotive force (mmf ) to set up the flux.
  • The core does not exhibit any eddy-current or hysteresis loss.
  • All the flux is confined to circulate within the core.
  • The resistance of each winding is negligible.

An ideal transformer

Bahaviour and Phasor diagram

The primary winding is connected to an alternating voltage source V1, while the secondary winding is left open. A current  Im  flows through the primary winding. Since the primary coil is pure inductive, the current  Im  lags behind the applied voltage V1  by 900. This current sets up alternating flux in the core and magnetises it. Hence it is called magnetising current. Flux is in phase with Im. The alternating flux links with both primary and secondary windings. When it links with primary, it produces self induced e.m.f. E1 in opposite direction to that of applied voltage V1 according to Lenz’s law. When this flux Φ links with secondary winding, it produces mutually induced e.m.f. E2 in opposite direction to that of applied voltage.

phasor diagram of an ideal transformer

Transformation Ratio

In an ideal transformer there is no power loss, so that, output must be equal to input.

E2I2cos Φ = E1I1cos Φ

E2I2 = E1I1

The induced emf in primary and secondary winding is directly proportional to number of primary and secondary winding turns.

E1 α N1

E2 α N2

The ratio of primary to secondary induced emfs is equal to the ratio of primary to secondary turns is called transformation ratio. It is denoted by letter K.

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