## Monday, June 3, 2013

### EMF Equation of Transformer

Figure 1 shows the representation of alternating flux, varying sinusoidally, which increases from its zero value to maximum value (Fm) in one-quarter of the cycle, that is in one-fourth of a second where f is the frequency of AC input in hertz.

The average rate of change of flux is given by , that is 4fFm Wb/s or V.
Figure 1 Representation of Alternating Flux
This rate of change of flux per turn is the induced emf in V.
Therefore, average emf/turn = 4fFmm V.

Let N1 and N2 be the number of turns in primary and secondary.

The rms value of induced emf in primary winding is given by
E1 = (4.44fFm m) × N1 = 4.44fFm mN = 4.44f BmArN1 (1.1)
where Ar is the area of cross-section.and
is the maximum value of flux density having unit Tesla (T) and Similarly, RMS value of induced emf in secondary winding is
E 2 = (4.44fFm )x N2 = 4.44fFmN2 = 4.44f BmArN2 (1.2)
From Equations (1.1) and (1.2), we have
N2/ N1= E2/ E1 = k
where ‘k’ is the turns ratio of the transformer,
i.e., k=N2/ N1
Equation (1.3) shows that emf induced per turn in primary and secondary windings are equal.
In an ideal transformer at no load, V1 = E1 and V2 = E2, where V2 is the terminal voltage of the transformer. Equation (1.3) becomes
If k>1 then the transformer is known as Step Up Transformer
If k<1 then the transformer is known as Step Down Transformer
If k>1 then the transformer is known as On-to-one or isolation Transformer