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 EMF Equation of the transformer is shown below
- 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
As 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
So the induced emf lags flux by 90 degrees.
The above equation is called the turn ratio where K is known as transformation ratio.
The equation (8) and (9) can also be written as shown below using the relation