# EMF Equation of a D.C. Generator

### DC Generator EMF Equation

Here we going to deduce an equation for DC generator output voltage.DC Generator EMF Equation explained in easy way below.

Let ,

Ø= flux/pole in webers

Z = total number of armature conductors

=Number of slots + Number of conductors per slot

P = number of poles
A = number of parallel paths in armature
[   A = 2 ... for wave winding &  A = P ... for lap winding ]
N = speed of armature in r.p.m.
Eg = EMF induced in any parallel path of armature.
As per Faraday’s law of electromagnetic induction.
Average e.m.f generated per conductor

= dØ/dt volts (N=1)  .......................(1)

During one revolution of armature in a ‘P’ pole generator, each armature conductor cuts the magnetic flux ‘P’ times so that flux cut per one conductor in one revolution is,

=dØ = PØ webers   .......................(2)

Armature revolves 60/N times one second. Therefore the time required by it for one revolution is dt.

i.e.,dt=60/N seconds   .......................(3)

EMF Equation of a D.C. Generator

Substituting equations (2) and (3) in equation (1), we get,

e.m.f generated/conductor = dØ/dt = (ØPN)/60 volts

The total number of armature conductors per parallel path=Z/A

The total EMF generated / path (Eg)= PØN/60*(Z/A)

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