__EMF Equation__- When an alternating voltage V
_{1}is applied to the transformer primary side, an alternating flux will set up in the core which links both primary and secondary winding. - This will result in self induced emf ( E
_{1}) sets up in the transformer primary winding and mutually induced emf ( E_{2}) sets up in the secondary winding.

Let

N

_{1}= Primary winding turns
N

_{2}= Secondary winding turns
Ф

_{m}= Maximum flux in the core ( Weber )
= B

_{m}× Ai
B

_{m}= Maximum flux density in the core ( Weber / meter^{2})
A

_{i}= Core area ( Meter^{2})
F = Frequency of alternating supply ( Hz )

- An alternating flux increases from zero to positive maximum in the one fourth of a cycle i.e. T/4 second
- According to Faraday’s law of electro – magnetic induction, the magnitude of induced emf is directly proportional to rate of change of flux linkages.

E α d ( NФ

_{m}) / dt
α N ( dФ

_{m }) / dt
Where

NФ

_{m}= Flux linkages
dФ

_{m}= Change in flux
dt = Change in time

- Therefore the average value of induced emf per turn is given by

E = ( Ф

_{m}– 0 ) / ( T / 4 )
= 4f Ф

_{m}- As the flux varies sinusoidally, the induced emf will be sinusoidal.
- Form factor = RMS Value / Average Value

= 1.11 ……………………( 1 )

( The value of form factor is 1.11 only for sinusoidal
waveform )

RMS value of induced emf per turn = Form factor × Average
emf

= 1.11 × 4f
Ф

_{m}
= 4.44f Ф

_{m}……….….….( 2 )
RMS value of induced emf in the transformer primary
winding

E

_{1}= 4.44f Ф_{m}× N_{1}
= 4.44f N

_{1}Ф_{m}……….…..( 3 )
Similarly the RMS value of induced emf in the transformer
secondary winding

E

_{2}= 4.44f Ф_{m}× N_{2}
= 4.44f N

_{2}Ф_{m}……………( 4 )
As we know that Ф

_{m}= B_{m}× A_{i}
E

_{1}= 4.44f B_{m}A_{i}N_{1}………….( 5 )
E

_{2}= 4.44f B_{m}A_{i}N_{2}………….( 6 )
From equation ( 5 ) and ( 6 )

E

_{1}/ E_{2}= N_{1}/ N_{2}…………..( 7 )
OR

E

_{1}/ N_{1}= E_{2}/ N_{2}= 4.44f B_{m}A_{i}………( 8 )
Equation ( 8 ) indicates that the induced emf per turn is
same in both primary and secondary winding.

__No Load Condition__
Under no load condition in the ideal transformer

V

_{1}= E_{1}and
V

_{2}= E_{2}**You may also like :**

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