EMF EQUATION OF TRANSFORMER

When a sinusoidal voltage is applied to the primary winding of a transformer, alternating flux ϕm sets up in the iron core of the transformer. This flux ϕm is of sinusoidal nature and it links with both primary and secondary winding.

Let

• ϕm be the maximum value of flux in Weber
• f be the supply frequency in Hz
• N1 is the number of turns in the primary winding
• N2 is the number of turns in the secondary winding

According to faraday’s law the induced emf in the windings can be written as

e = - N * dⲪ/dt

e = -N * d (Ⲫₘ sin ⍵t) / dt

e = -N * ⍵ * Ⲫₘ cos ⍵t ............(1)

As we can write cosωt as sin(  – ωt) but as we can see there is negative sign in the above equation it will be modified like this

e = N * ⍵ * Ⲫₘ sin(⍵t - 𝜋/2) ...........(2)

Equation (2) may be written as

e = Eₘ sin(⍵t - 𝜋/2) ............(3)

Where Eₘ (=N * ⍵ * Ⲫₘ)  is the maximum value of induced emf.

For a sine wave, the r.m.s value of the e.m.f. is given by 

E_rms  = E = Eₘ / √2

E = N * ⍵ * Ⲫₘ / √2

E = N * (2 * 𝜋 * f) *Ⲫₘ / √2

E = 4.44 * Ⲫₘ * f * N ...........(4)

Equation (4) is called the e.m.f. equation of a transformer.

The value of induced emf depends upon flux, number of turns and frequency.

Now if someone want to write the emf equation for primary and secondary sides then simply put subscripts 1 and 2 as shown below

The primary r.m.s. voltage is

E₁ = 4.44 * Ⲫₘ * f * N₁ .......(5)

The secondary r.m.s. voltage is

E₂ = 4.44 * Ⲫₘ * f * N₂ ..........(6)

Thanks for Reading.