# EMF Equation for a Transformer

### EMF Equation for a Transformer

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,

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 m volts

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

E2 = 4.44 N2 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. 