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 = ZΦPN / 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