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EMF EQUATION OF A TRANSFORMER

The magnetic flux ϕ set up in the core of a transformer when an alternating voltage is applied to its primary winding is also alternating and is sinusoidal.

Let ϕm be the maximum value of the flux and f be the frequency of the supply. The time for 1 cycle of the alternating flux is the periodic time T, where T = (1/f) seconds

The flux rises sinusoidally from zero to its maximum value in (1/4) cycle, and the time for (1/4) cycle is (1/4f) seconds. Hence the average rate of change of flux = (ϕm/ (1/4f)) = 4f ϕm Wb/s, and since 1Wb/s D 1 volt, the average emf induced in each turn = 4f ϕm volts. As the flux ϕ varies sinusoidally, then a sinusoidal emf will be induced in each turn of both primary and secondary windings.
For a sine wave,
Form Factor = r.m.s Value / Average Value
= 1.11
Hence r.m.s. value = form factor*average value = 1.11 * average value Thus r.m.s. e.m.f. induced in
each turn
=1.11 * 4fϕm volts
=4.44fϕm volts
Therefore, r.m.s. value of e.m.f. induced in primary,
E1 = 4.44 f ϕmN1 volts
and r.m.s. value of e.m.f. induced in secondary,
E2 = 4.44 f 8ϕN2 volts
Dividing E1 by E2
E1E2=N1N2

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