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E.M.F. Equation


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Here you can find all types notes by handwritten.
Here,we are providing physics E.M.F.
effect,which is most useful in your semester exam.This topic is totally designed according to our syllabus.
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EMF Equation of a Transformer

When a sinusoidal voltage is applied to the primary winding of a transformer, alternating flux Ï•m sets up in the iron core of the transformer. This sinusoidal flux links with both primary and secondary winding. The function of flux is a sine function.
The rate of change of flux with respect to time is derived mathematically.
The derivation of the EMF Equation of the transformer is shown below. Let
  • Ï•m be the maximum value of flux in Weber
  • f be the supply frequency in Hz
  • N1 is the number of turns in the primary winding
  • Nis the number of turns in the secondary winding
Φ is the flux per turn in Weber
emf-eq-of-transformer-figureAs shown in the above figure that the flux changes from + Ï•m to – Ï•m in half a cycle of 1/2f seconds.
By Faraday’s Law
Let E1 be the emf induced in the primary winding
emf-eq-1
Where Ψ = N1ϕ
emf-eq-2
Since Ï• is due to AC supply Ï• = Ï•Sinwt
emf-eq-3
So the induced emf lags flux by 90 degrees.
Maximum valve of emf
emf-eq-4
But w = 2Ï€f
emf-eq-5
Root mean square RMS value is
emf-eq-6
Putting the value of E1max in equation (6) we get
emf-eq-7
Putting the value of Ï€ = 3.14 in the equation (7) we will get the value of E1 as
emf-eq-8
Similarly
emf-eq-9
Now, equating the equation (8) and (9) we get
emf-eq-10
The above equation is called the turn ratio where K is known as the transformation ratio.
The equation (8) and (9) can also be written as shown below using the relation
(Ï•m = Bm x Ai) where Ais the iron area and Bm is the maximum value of flux density.
emf-eq-11
For a sinusoidal waveemf-eq-12

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