EMF Equation of Transformer

Figure 1 shows the representation of alternating flux, varying sinusoidally, which increases from its zero value to maximum value (F_m) in one-quarter of the cycle, that is in one-fourth of a second where f is the frequency of AC input in hertz.

The average rate of change of flux is given by , that is 4fF_m Wb/s or V.

Figure 1 Representation of Alternating Flux

This rate of change of flux per turn is the induced emf in V.

Therefore, average emf/turn = 4fF_mm V.

Let N₁ and N₂ be the number of turns in primary and secondary.

The rms value of induced emf in primary winding is given by

E₁ = (4.44fF_m m) × N₁ = 4.44fF_m mN = 4.44f B_mA_rN₁ (1.1)

where A_r is the area of cross-section.and

 is the maximum value of flux density having unit Tesla (T) and Similarly, RMS value of induced emf in secondary winding is

E ₂ = (4.44fF_m )x N₂ = 4.44fF_mN₂ = 4.44f B_mA_rN₂ (1.2)

From Equations (1.1) and (1.2), we have 

N_2/ N1= E_2/ E1 = k

where ‘k’ is the turns ratio of the transformer,

i.e., k=N_2/ N1

Equation (1.3) shows that emf induced per turn in primary and secondary windings are equal.

In an ideal transformer at no load, V₁ = E₁ and V₂ = E₂, where V₂ is the terminal voltage of the transformer. Equation (1.3) becomes

If k>1 then the transformer is known as Step Up Transformer

If k<1 then the transformer is known as Step Down Transformer

If k>1 then the transformer is known as On-to-one or isolation Transformer