EMF Equation of Power Transformer


Whenever we apply an alternating current to the primary of a power transformer there will be an alternating flux created inside the transformer core. The flux inside the transformer core will link with both of the primary and secondary windings. Since the flux is also alternating, it changes its magnitude continuously. Therefore, the linkage of the changing magnetic flux with the winding turn causes the induction of EMF in the turn. It happens according to Faraday’s Laws of electromagnetic induction. Therefore from the expression of the flux in the core, we can easily determine the EMF equation of a power transformer.

 

Since the supply current is sinusoidal in nature, the magnetic flux produced by it is also sinusoidal. Let us considered the expression of the flux is as follows.

EMF equation of power transfer 1

Now, according to Faraday’s law of electromagnetic induction, the rate of change of flux linkage with respect to time is directly proportional to the induced EMF. Therefore, the expression of the induced EMF per turn in the winding is as follows.

EMF equation of power transfer 2

Here, we have given a minus sign. This minus sign is according to Lenz’s law. Although we are not going to discuss the law in detail in this article of EMF equation of power transformer, just we should remember that according to this law the induced EMF opposes the source voltage. This is the reason the minus sign comes here.

The same flux links with both primary and secondary windings. The above-mentioned expression of EMF per turn is the same for both primary and secondary windings.

EMF Equation of Power Transformer against Primary Winding

Suppose, T1 is the number of turns in the primary winding. Therefore the expression of the total EMF induced the primary winding is

EMF equation of power transfer 3

The above expression represents the instantaneous value of the induced EMF across the primary winding. This is also a sinusoidal waveform. Therefore the magnitude of the waveform is

EMF equation of power transfer 4

From here, we can write The RMS value of the EMF as

EMF equation of power transfer 5

From the above equation also we can see that the EMF per turn is

EMF equation of power transfer 6

EMF Equation of Power Transformer against Secondary Winding

As we have already told that the EMF per turn is irrespective of the windings. It is the same for both the primary and secondary windings. Therefore, the ultimate expression of the EMF across the secondary winding is

EMF equation of power transfer 7

Where T2 is the number of secondary turns of the power transformer.

Sharing is caring!

Make a comment and if there is any any grammatical or technical error on the post please let us know with your comments.

avatar
  Subscribe  
Notify of
shares