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D.C Generator E.M.F Equation

**E.M.F Equation**

Derive the emf equation of a DC generator.
**E= dΦ/dt = ****ZΦN/60 x P/A Volt**
Where, Φ = flux/pole in wb; Z = total number of armature conductors
= No.of slots x No.of conductors/slot; P = No.of generator poles; A = No.of parallel paths in armature; N = armature rotation in revolutions per; minute (RPM); E = e.m.f induced in any parallel path in armature

Let
Φ = flux/pole in wb
Z = total number of armature conductors = No.of slots x No.of conductors/slot
P = No.of generator poles
A = No.of parallel paths in armature
N = armature rotation in revolutions per minute (RPM)
E = e.m.f induced in any parallel path in armature

Then
Generated e.m.f Eg = e.m.f generated in any one of the parallel paths i.e E.

Average e.m.f geneated /conductor = **dΦ/dt **volt (n=1)

Now, flux linkage per conductor in one revolution **dΦ = ΦP **Wb
No.of revolutions per second = N/60
Time for one revolution, **dt = 60/N** second
Hence, according to Faraday's Laws of Electromagnetic Induction,
**E.M.F generated/conductor is**
**dΦ/dt = ****ΦPN/60**

For a **wave-wound **generator
No.of parallel paths (A)= 2
No.of conductors (in series) in one path = Z/2
E.M.F. generated/path is given by

**E = ΦPN/60 x Z/2** = **Z**ΦPN / 120 volt

For a **lap-wound** generator
No.of parallel paths (A) = P
No.of conductors (in series) in one path = Z/P
E.M.F.generated/path
**E** = **ΦPN/60 x Z/P** = **ZΦN / 120** Volt

In general generated e.m.f
**E= dΦ/dt = ****ZΦN/60 x P/A Volt**

where A = 2 - for wave-winding
= P - for lap-winding