Electrical Engineering ⇒ Topic : E.M.F. Equation of a Transformer

E.M.F. EQUATION OF A TRANSFORMER

Let us assume that N₁ is the number of turns in primary winding, N₂ is the number of turns in secondary winding, B_m is the maximum value of flux density, A' is area of cross-section of the core, and f is the frequency of supply voltage.

Let the instantaneous flux be given by

            Φ = Φ_m sin ωt                   .............(1)

where Φ _m is the maximum value of the flux in the core and Φ _m = B_mA'.

Figure (a) shows the variation of flux in the core.

                   figure (a)Variation of flux with time

Since Φ  is zero at t = 0 and Φ = Φ_m at t = T/4, i.e., t= 1/4f.Therefore, average rate of change of flux is given by

            ................... (1)

                                                                                             ................... (2)

From Eqs. (1) and (2), we have

                                                    ............. (3)