Q. Derive the expression for generated emf in a dc generator.

Ans.

Expression for Generated emf in a DC Generator

             We shall now derive an expression for the emf generated in a d.c. generator.

                   Let Φ    = flux/pole in Wb

                          Z    = total no. of armature conductors

                          P    = no. of poles

                          A   = no. of parallel paths = 2......for wave winding

                                = P....for lap winding

                          N   = speed of armature in r.p.m.

                          E_g   = e.m.f. of the generator = e.m.f./parallel path

             Flux cut by one conductor in one revolution of the armature, dΦ = pΦ webers

                     Time taken to complete one revolution,

                           dt = 60/n sec.

                    e.m.f. generated/conductor  dΦ/dt =  PΦ/60/N = PΦN/60 volts

                    e.m.f. generator, E_g = e.m.f. per parallel path

                                  = (e.m.f/conductor) × No. of conductor in series per parallel path

                                  =   PΦN/60 × Z/A

                          E_g    =   PΦZN/60A

                        A       = Z...for wave winding

                                  = P....for lap winding