DC Generator Operating Principle - e.m.f. Equation

The basic principle of a DC machine is Faraday's laws of electromagnetic induction. According to these law, when an conductor moves in a magnetic field it cuts magnetic lines force, due to which an emf is induced in the conductor. The magnitude of this induced emf depends upon the rate of change of flux (magnetic line force) linkage with the conductor.When the armature rotates, the armature conductors cut the flux produced by the field windings (poles). Hence an emf is induced in the armature winding. The direction of induced current is given by Fleming’s right hand rule.

  

Let          Φ – Flux per pole in Wb

               Z – total number of conductors on the armature

               P – number of poles

               A – number of parallel paths on the armature

                           ( = P for Lap and = 2 for Wave)

               N – Speed of rotation of armature in rpm

               E – average emf induced

Then, total flux cut by a conductor taking one complete revolution,

d Φ = P Φ

Time taken for one complete revolution,

                        dt = 60/N seconds

According to faradays law of electromagnetic induction,

Emf induced per conductor,

                 

If there is Z number of conductors connected in A number of parallel paths,

                volts

Since, A, P, Z are constants,

                        E α N Φ