[2023] All About EMF Equation of Transformer Explained

    EMF equation of the transformer is the mathematical expression used to determine the magnitude of induced emf in the winding of the transformer. Consider N₁ and N₂ are the number of turns of the transformer's primary and secondary winding.

    When we supply an alternating voltage V₁ of frequency f to the primary winding an alternating magnetic flux (ϕ) is produced by the primary winding in the core of the transformer. This alternating magnetic flux (ϕ) links with both primary and secondary winding of the transformer. As ac voltage is sinusoidal in nature then, the magnetic flux can be given by

ϕ = ϕ_msinωt------(1)

    where,

ϕ is the alternating flux produced by the primary winding in the core of the transformer

ϕ_m is the amplitude of the flux produced i.e. maximum value of the flux produced

ω is the angular frequency

t is the time period

    Now, according to the principle of electromagnetic induction instantaneous value of emf induced in the primary winding is given by

E₁ = -N₁ ( dϕ / dt )

or, E₁ = -N₁ ( d(ϕ_msinωt) / dt )

or, E₁ = -N₁ωϕ_mcosωt

    since,

-cosωt = sin(ωt-90)

ω = 2πf

or, E₁ = 2πfN₁ϕ_msin(ωt-90)

above equation can be written as

 E₁ = E_m1sin(ωt-90)------(2)

    where,

E_m1 = 2πfN₁ϕ_m is the maximum value of the induced EMF E₁ 

    Now for sinusoidal supply, the RMS value of EMF of the primary winding( E₁ ) is given by,

E₁ = (E_1m) / sq.rt(2)

or, E₁ = ( 2πfN₁ϕ_m ) / sq.rt(2)

or, E₁ = 4.44fN₁ϕ_m 

    Similarly, the RMS value of the EMF of the secondary winding (E₁) is given by,

E₂ = 4.44fN₂ϕ_m 

    Generally,

E = 4.44fNϕ_m is known as EMF equation of the transformer.

Conclusion

    Hope, you have clearly understand about the EMF equation of the transformer. Make sure to leave your opinion and suggestion about this post in the comment section.