EMF Equation of a Transformer



Let an alternating voltage source V1  be connected to the primary winding of a transformer. Now, due to the voltage source V ,an alternating current  I   starts flowing through N1 turns. 


emf equation of  transformer


The current I  through primary winding produces  mmf  equal to  N1 I
But from magnetic circuits basics,       flux = mmf / reluctance

Therefore,   Î¦ =  N1I  / reluctance

Since, the magnetic flux path reluctance remains almost constant throughout the operation of the transformer and N1  is also constant, therefore
Φ ∝ I
Therefore, an alternating sinusoidal flux is produced.

EMF Equation of a Transformer




Let the sinusoidally varying flux be expressed as
Φ= Φmax sinwt
where,
Φmax = maximum value of core flux
w = 2Ï€f , angular frequency of source V1


On Primary side :-

By faraday’s law of electromagnetic induction, emf induced in primary is 
emf equation of  transformer

emf equation of  transformer


emf equation of a transformer




Showing that emf per turn in primary is equal to emf per turn in secondary of a transformer. From this concept you can also find which side is high voltage side (more number of turns) and which is low voltage side  (less number of turns) by just looking at a transformer.



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