EMF Equation of a 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 sinusoidal flux links with both primary and secondary winding. The function of flux is a sine function.

The rate of change of flux with respect to time is derived mathematically.

The derivation of the EMF Equation of the transformer is shown below. 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

Φ is the flux per turn in Weber
emf-eq-of-transformer-figureAs shown in the above figure that the flux changes from + ϕm to – ϕm in half a cycle of 1/2f seconds.

By Faraday’s Law

Let E1 be the emf induced in the primary winding

Where Ψ = N1ϕ

Since ϕ is due to AC supply ϕ = ϕm Sinwt

So the induced emf lags flux by 90 degrees.

Maximum valve of emf

But w = 2πf

Root mean square RMS value is

Putting the value of E1max in equation (6) we get

Putting the value of π = 3.14 in the equation (7) we will get the value of E1 as


Now, equating the equation (8) and (9) we get

The above equation is called the turn ratio where K is known as the transformation ratio.

The equation (8) and (9) can also be written as shown below using the relation

(ϕm = Bm x Ai) where Ai is the iron area and Bm is the maximum value of flux density.

For a sinusoidal waveemf-eq-12

Here 1.11 is the form factor.

33 thoughts on “EMF Equation of a Transformer”

  1. Rajeshwari Shekhawat

    How to calculate number of turns in the primary coil of a transformer if the following is given:-
    1. Voltage primary side
    2. Core cross section area
    3. Current in primary coil

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