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Electrical Engineering and Instrumentation - Induction Machines and Synchronous Machines

**Equation of Induced EMF**

Let Φ = Flux per pole, in Wb

P =
Number of poles

N_{s}
= Synchronous speed in r.p.m.

f =
Frequency of induced e.m.f. in Hz

Assume
full pitch winding for simplicity i.e. this conductor is connected to a
conductor which is 180^{o} electrical apart. So there two e.m.f.s will
try to set up a current in the same direction i.e. the two e.m.f. are helping
each other and hence resultant e.m.f. per turn will be twice the e.m.f. induced
in a conductor.

**. ^{.}. **E.m.f. per turn = 2 x (e.m.f. per
conductor)

= 2 x (2 f
Φ)

= 4 f Φ
volts

Let T_{ph}
be the total number of turn per phase connected in series. Assuming
concentrated winding, we can say that all are placed in single slot per pole
per phase. So induced e.m.f.s in all turns will be in phase as placed in single
slot. Hence net e.m.f. per phase will be algebraic sum of the e.m.f.s per turn.

Average E_{ph}
= T_{ph} x (Average e.m.f. per turn)

Average
Eph = T_{ph} x 4 f Φ

But in
a.c. circuits R.M.S. value of an alternating quantity is used for the analysis.
The form factor is 1.11 of sinusoidal e.m.f.

K_{f} =
(R.M.S.)/Average = 1.11 ......... for
sinusoidal

**. ^{.}.** R.M.S.
value of E

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