EMF equation of transformers lets you calculate the RMS values of induced voltages in the primary and secondary windings of a transformer. An alternating voltage, when applied to the primary of a transformer, produces an alternating magnetic field which induces EMF in the secondary windings.

The produced magnetic flux is alternating in nature and lags the applied voltage by 90^{0}. However, the flux remains in phase to the magnetizing current. The instantaneous value of flux is given by

Where, φ_{max} is the maximum value of flux produced and ωt is the time period.

The instantaneous value of the applied voltage is given by

Where, v_{1} is the applied voltage and ‘+π/2’ indicates that the voltage leads the flux.

If N_{1} and N_{2} are the numbers of primary and secondary turns, the EMF inducing in the primary and secondary winding are given by:

Therefore

Similarly,

e_{1} and e_{2} are the EMF equations of primary and secondary coils of a transformer. In general, the EMF equation of transformers is as follows:

## Voltage transformation ratio of a transformer

Voltage transformation ratio of a transformer is the ratio of primary and secondary voltages.