The armature conductors are generally connected in two different ways, viz. lap winding and wave winding. For lap wound armature, the number of parallel paths is equal to the number of poles
EMF EQUATION
Let
φ be the flux per pole in webers.
Let
P be the number of poles.
Let
Z be the total number of conductors in the armature. All the Z conductors are
not connected in series. They are divided into groups and let A be the number
of parallel paths into which these conductors are grouped.
So
each parallel path will have Z/A conductors in series.
Let
N be the speed of rotation in revolutions per minute (rpm).
Consider
one conductor on the periphery of the armature. As this condition makes one
complete revolution, it cuts Pφ in webers.
As
the speed N is N rpm, the time taken for one revolution is 60/N secs.
Since
the emf induced in the conductor = rate of change of flux cut.

Since
there are Z/A conductors in series parallel path, the emf induced,

The
armature conductors are generally connected in two different ways, viz. lap
winding and wave winding. For lap wound armature, the number of parallel paths
is equal to the number of poles (i.e., A = P). In wave wound machines, A = 2
always.
Electrical and Instrumentation Engineering: Unit II: DC Machines : Tag: : Derivation - EMF Equation of DC Machines
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