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My textbook says that when primary winding of an ideal transformer is connected to an alternating voltage, an alternating current flows which in turn produces an alternating flux which causes an EMF to be induced in the primary coil which is equal and opposite to the applied voltage. Now how can current flow, if the applied EMF and the back EMF generated in the primary coil are equal? Also if we take an ideal transformer, the resistance of the windings will be zero and if it is zero then the current in windings will become infinite which is something I am not able to grasp. Please explain in detail. Thanks in advance.

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    – hyportnex
    Nov 9, 2016 at 17:31

2 Answers 2

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An ideal transformer, as the name implies, is not a real object. Thus, in an ideal transformer there are no windings, no core, nothing.

An ideal transformer is an element which is indirectly defined only through the constitutive equations

$$\begin{align}v_2 &= \frac{1}{n}v_1, \\ i_2 &= -ni_1, \end{align}$$

where the reference directions of voltages and currents are chosen according to the convention of multiport devices.

And because of this, the ideal transformer works also in DC!

That said, an ideal transformer can be seen as a limiting case of a pair of lossless coupled inductors with a coupling coefficient of 1 when the primary inductance goes to infinity. In this limit, the current in the primary winding tends to zero when the primary inductance tends to infinity, if the secondary winding is not loaded.

I discussed this limiting case in this answer.

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Now how can current flow, if the applied EMF and the back EMF generated in the primary coil are equal?

Because they are equal only in ideal transformer (ideal wires without dissipation). Then extremely small remaining force is needed to move the electrons, as they are very light. This extremely small force is customarily neglected in discussion of current in ideal conductors.

In real conductors and real transformers, there is dissipation of energy, electrons experience resistance to motion, so actually induced EMF does not counteract the applied electrostatic field exactly, but some non-zero force remains. This remaining force pushes the current against the dissipative forces like Ohmic resistance.

Also if we take an ideal transformer, the resistance of the windings will be zero and if it is zero then the current in windings will become infinite which is something I am not able to grasp.

Resistance being zero does not imply current will become infinite. Infinite current would require infinite energy which is not easily available, so current will only get as high as available energy and physical laws allow.

In ideal conductor with zero resistance, current is limited by external conditions and laws such as the Faraday law. Current can increase, but this will cause induced EMF to be present, which means somebody has to supply work to increase the current. As a result, current does not get arbitrarily high because nobody can supply arbitrary amounts of work.

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