Answer:

EMF equation of 1-phase transformer:

• We know that the EMF Induced in each turn of coil,$e=\dfrac{\mathrm d\phi}{\mathrm dt}\dots \dots \dots \dots\mathrm {Equation \ (1)}$
• Where, $\mathrm d\phi$ is the change in flux linkage & $dt $ is the time during which the flux linkage is changed.
• When the transformer is connected to a single  phase A.C. supply an alternating flux, as shown in figure below is induced in transformer core.

• If we analyze the flux wave form given above, flux change from 0 to $\phi_m$   in $\dfrac{T}{4}$  time, where T is the time period.
• Hence,$\mathrm d\phi=\phi_m\quad and\quad \mathrm dt = \dfrac{T}{4}\quad$substituting these values in equation (1)

$e=\dfrac{\phi_m}{\Big[\dfrac{T}{4}\Big]}$

or  $e=\dfrac{4\phi_m}{{T}}\dots \dots \dots\mathrm {Equation\ (2)}$

• As Time period, $T=\dfrac{1}{f}$
• Where, $f$ is the frequency of sinusoidal flux induced in core. * Hence, EMF induced in each turn of coil, $ e=4\phi_m f\dots \dots \dots \mathrm {Equation \ (3)}$ * If, primary & secondary of transformer is having $\mathrm {N_1 \ and \ N_2}$ number of turns respectively, * Then EMF induced in primary, $ e_1=4\phi_m fN_1\dots(4)$ & EMF induced in secondary,$ e_2=4\phi_m fN_2\dots(5)$