When a primary of a transformer connected to the ac supply, an alternating flux is set up in the core which links with primary and secondary winding.

Let,

Φ_{m} = maximum value of flux in Weber.

F = supply frequency in Hz

N_{1 }= number of turns in primary

N_{2 }= number of turns in secondary

E_{1 }= e.m.f. induced in primary

E_{2 }= e.m.f. induced in secondary

Flux changes from +Φ_{m} to 0 in one forth a cycle *i.e. *1/4f seconds, as shown in figure

Average rate of change of flux

= *4fΦ _{m} *Wb/sec

Now, the rate of change of flux per turn is the average induced e.m.f. per turn in volts.

∴ Aveage e.m.f. induced per turn = *4fΦ _{m} *volts

∴ R.M.S. value of em.f. induced per turn *E = *1.11 × *4fΦ _{m }= 4.44 fΦ_{m }volts*

Since primary and secondary have *N _{1 }*and

*N*

_{2 }turns respectively.Therefore, R.M.S. value of e.m.f. in primary,

E_{1 }= 4.44 N_{1} *fΦ _{m }volts*

Therefore, R.M.S. value of e.m.f. in secondary,

E_{2 }= 4.44 N_{2} *fΦ _{m }volts*

*From above equation, we concluded that induced emf primary and secondary winding is directly proportional to the number of turns, supply frequency and value of flux. *