Let               N₁ = No. of  turns in primary

                       N₂ = No. of  turns in secondary

                      Ø_m = Maximum flux in core in webers = B_m x A

                        f  = Frequency of a.c. input in Hz.

    The flux increases from it's zero value to maximum value Ø_m  in one quarter of the cycle i.e. in 1/4 f second.

    Therefore, r.m.s value of e.m.f./turn = 4.44 Ø_m volts

  Now, r.m.s value of induced e.m.f in the whole primary winding 

                                        = ( induced e.m.f. / turn ) x No. of primary winding

                                   E₁ = 4.44 f N₁Ø_m     -------------------  ( i )

    Similarly, r.m.s. value of e.m.f. induced in secondary is,

                                   E₂ = 4.44 f N₂Ø_m     -------------------  ( ii )    

From the above equations (i) and (ii), we get

                                 =  K 

(i)   If    K>1, then the transformer is called step-up transformer.

(ii)   If    K<1, then the transformer is called step-down transformer.