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
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 the transformation ratio.
The equation (8) and (9) can also be written as shown below using the relation
Here 1.11 is the form factor.