EMF Equation of a Transformer

EMF EQUATION OF A TRANSFORMER

The primary winding of a transformer excited by alternating voltage V₁, it produce an alternating flux ϕ. The primary winding has N₁ number of turns. The flux links the secondary winding through the common magnetic core. It produces induced emf in the secondary. Let us derive the equation for E₁ and E₂.

N₁ = no.of turns in primary

N₂ = no.of turns in secondary

ϕ_m = maximum flux in core in webers

=B_m × A

ƒ = frequency of AC input in Hz

As the Figure 3.48 shows, flux increases from its zero value to maximum value ϕ_m in one quater of the cycle.

Average rate of change of flux = 

= 4ƒϕ_m wb/s

rate of change of flux per turn means induced emf in volts.

Average emf/turn = 4ƒϕ_m volts

If flux ϕ varies sinusoidally, then rms value of induced emf is obtained by multiplying the average value with form factor.

From factor = rms value/average value = 1.11

rms value of emf/turn= 1.11 x 4ƒϕ_m

= 4.44 ƒϕ_m volts

RMS value of the induced emf in the whole of primary winding

= [induced emf/turn] × No.of primary winding

= 4.44 ƒϕ_m N₁

E₁ = 4.44 ƒB_m A N₁ ……….(1)

Similarly rms value of the emf induced in secondary is

E₂ = 4.44 ƒ N₂ ϕ_m

E₂ = 4.44 ƒ B_m AN₂………….(2)

From equation (1) and (2) that

E₁/N₁ = E₂/N₂ = 4.44 ƒ ϕ_m

It means that emf/turn is the same in both the primary and secondary windings.

In an ideal transformer on no-load

V₁ = E₁ and E₂ = V₂.