EMF Equation of a Transformer

Let,

N₁= No. of turns in primary Winding

N₂= No. of turns in secondary Winding

Φ_m = Maximum flux in core in webers

       = B_m x A

F = Frequency of AC input in Hz.

In the fig. flux rises from its value zero to maximum Φ_m 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 Φ_m 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 Φ_m

                              = 4.44 f Φ_m 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 Φ_m = 4.44fN₁ B_m A ---->1

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Similarly, r.m.s. value of the e.m.f. induced in secondary is,

E2 = 4.44fN2 Φ_m = 4.44fN₂ B_m A ---->2

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

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

CSV Oct 4, 2013

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