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.
Φm = maximum value of flux in Weber.
F = supply frequency in Hz
N1 = number of turns in primary
N2 = number of turns in secondary
E1 = e.m.f. induced in primary
E2 = e.m.f. induced in secondary
Flux changes from +Φm to 0 in one forth a cycle i.e. 1/4f seconds, as shown in figure
Average rate of change of flux
= 4fΦm 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 = 4fΦm volts
∴ R.M.S. value of em.f. induced per turn E = 1.11 × 4fΦm = 4.44 fΦm volts
Since primary and secondary have N1 and N2 turns respectively.
Therefore, R.M.S. value of e.m.f. in primary,
E1 = 4.44 N1 fΦm volts
Therefore, R.M.S. value of e.m.f. in secondary,
E2 = 4.44 N2 fΦm 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.