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# EMF Equation of Transformer

## EMF Equation of Transformer

Let
N1 = Number of turns in primary windings.
N2 = Number of turns in second windings.
• = Maximum flux in the core in Webbers.
• m= Bm.A,
f = Frequency of A.C input in Hz.
As shown in fig- flux increases from its zero value to maximum value Øm  in one quarter of the cycle i.e. in ¼ second.
Average rate of change of flux = (Øm / ¼f.)
= 4f Øm Wb/s or volt.

Now rate of change of flux per turn means induced e.m.f in volts.
Average e.m.f /per turn = 4f Øm volt.
If flux Øm 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 Øm= 4.44f Øm volt
now r.m.s value of the induced e.m.f in the whole primary winding.
=( induced e.m.f/turn) . number of primary turns
E1 = 4.44fN1 Øm………………………………………(1)
E1 = 4.44fN1BmA.    (Øm= BmA)

Similarly, r.m.s value of the e.m.f. induced in secondary is,
E2 = 4.44fN2 Øm
E2 = 4.44fN2BmA.    (Øm= BmA)…………..(2)

It’s seen from (1) and (2) that E1/N1=E2/N2= = 4.44f Øm.  It means that e.m.f/ turn is the same is the same in both the primary and secondary windings.
So in ideal Transformer on no-load, V1=E1 and E2=V2 where E2 is the terminal voltage.
By : Engr Wasim Khan

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