# EMF Equation of a Transformer

Let,
N1= No. of turns in primary Winding
N2= No. of turns in secondary Winding
Φm = Maximum flux in core in webers
= Bm x A
F = Frequency of AC input in Hz.

In the fig. flux rises from its value zero to maximum Φm value in one quarter of the cycle i.e. in 1/4 f second.

Average rate of change of flux = Φm /1/4f
= 4 Wb/s or volt
Now, rate of change of flux per turn means induced e.m.f. in volts.
Average e.m.f./turn = 4 f Φm volts

If flux Φ varies sinusoidally, then r.m.s. value of induced e.m.f. is obtained by multiplying the average value with form factor.

Form factor = r.m.s. value / average value   =1.11

r.m.s. value of e.m.f./turn = 1.11 × 4 f Φm
= 4.44 f Φm volt.

Now, r.m.s. value of the induced e.m.f. in the whole of primary winding
= (induced e.m.f/turn) × No. of primary turns

E1 = 4.44fN1 Φm = 4.44fN1 Bm A ---->1
Similarly, r.m.s. value of the e.m.f. induced in secondary is,
E2 = 4.44fN2 Φm = 4.44fN2 Bm A ---->2

From the equation 1 ----> 2 that E1/N1 = E2/N2 = 4.44f Φm.

It means that e.m.f./turn is the same in both the primary and secondary windings.
In an ideal transformer on no-load, V1=E1 and E2=V2. Where V2 is the terminal voltage