When an alternating voltage V_{1} is applied to a primary winding, an alternating current I_{1 }flows in it producing an alternating flux in the core. As per Faraday’s laws of electromagnetic induction, an emf e_{1} is induced in the primary winding.

**Working Principle of a transformer**

e_{1} = \(-N_1\frac{d\varphi}{dt}\)

Where N_{1 }is the number of turns in the primary winding. The induced emf in the primary winding is nearly equal and opposite to the applied voltage V_{1}.

Assuming leakage flux to be negligible, almost the flux produced in primary winding links with the secondary winding. Hence, an emf e_{2} is induced in the secondary winding.

e_{2} = \(-N_2\frac{d\varphi}{dt}\)

Where N_{2 }is the number of turns in the secondary winding. If the secondary circuit is closed through the load, a current I_{2} flows in he secondary winding. Thus energy is transferred from the primary winding to the secondary winding.

**EMF EQUATION.**

As the primary winding is excited by a sinusoidal alternating voltage, an alternating current flows in the winding producing a sinusoidally varying flux \(\varphi\) in the core.

\(\varphi\,=\,\varphi msin\omega t\)

As per Faraday’s law of electromagnetic induction an emf e_{1} is induced in the primary winding.

e_{1} = \(-N_1\frac{d\varphi}{dt}\)

e_{1} = \(-N_1\frac{d\varphi}{dt}\)(\(\varphi msin\omega t\))

Maximum value of induced emf = \(2\pi f \varphi_mN_1\)

Hence, rms value of induced emf in primary winding is given by,

E_{1} = \(\frac{Emax}{\sqrt2}\) = \(\frac{2\pi fN_1 \varphi_m}{\sqrt2}\) = 4.44fN_{1}\(\varphi_m\)

Similarly rms value of induced emf in the secondary winding is given by,

E_{2}_{ }= 4.44\(fN_2\varphi_m\)

Also,\(\frac{E_1}{N_1}\) = \(\frac{E_2}{N_2}\) = 4.4f\(\varphi_m\)

Thus emf per turn is same in primary and secondary winding and an equal emf is induced in each turn of the primary and secondary winding.