Figure 1 shows the representation of alternating flux, varying sinusoidally, which increases from its zero value to maximum value (

*F*) in one-quarter of the cycle, that is in one-fourth of a second where_{m}*f*is the frequency of AC input in hertz.
This rate of change of flux per turn is the induced emf in V.

Therefore, average emf/turn = 4

*fF*m V._{m}
The rms value of induced emf in primary winding is given by

*E*

_{1}= (4.44

*fF*m) ×

_{m}*N*

_{1}= 4.44

*fF*mN = 4.44

_{m}*f B*

_{m}A_{r}N_{1}(1.1)

where

is the maximum value of flux density having unit Tesla (T) and Similarly, RMS value of induced emf in secondary winding is

*A*is the area of cross-section.and_{r}is the maximum value of flux density having unit Tesla (T) and Similarly, RMS value of induced emf in secondary winding is

*E*

_{2}= (4.44

*f*

*F*)x

_{m}*N*

_{2}= 4.44

*fF*

_{m}*N*

_{2}= 4.44

*f*

*B*

_{m}A_{r}N_{2}(1.2)

From Equations (1.1) and (1.2), we have

where ‘

*k*’ is the turns ratio of the transformer,
i.e., k=

*N*_{2/ }*N1*
Equation (1.3) shows that emf induced per turn in primary and secondary windings are equal.

In an ideal transformer at no load,

*V*_{1}=*E*_{1}and*V*_{2}=*E*_{2}, where*V*_{2}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