Problems related to EMF equation of DC generator

1. In a 4 pole DC generator, the number of conductors is 600 and
flux per pole is 0.02 Wb and speed is 1600 rpm. (a) calculate the
generated emf if the armature is connected in (i) wave wound
(ii) Lap wound
No of Poles, P = 4
No. of conductors, Z = 600
Flux/pole, ϕ = 0.02 wb
Speed, N = 1600 rpm
(a)For Lap winding
No of parallel path A = P
Generated emf , Eg =
∅ZN P
60 A
=
0.02 ×600 × 1600 ×4
60 ×4
= 320V
(b) For wave winding
No of parallel path A = 2
Generated emf , Eg =
∅ZN P
60 A
=
0.02 ×600 × 1600 ×4
60 ×2
= 640V

2. Lap winding; the ends of each armature coils are connected to adjacent
segments on the commutators
so that the total number of parallel paths (A) = total no.of poles (P)
Lap winding A = P
Use in Low voltage high current machines
Wave winding; the ends of each armature coils are connected to
adjacent segments some distance apart, and only two parallel paths are
provided between positive and negative brushes.
For Wave winding A = 2
Use in High voltage Low current machines
Lap Winding
Wave winding

3. A 4 pole DC generator having wave wound armature winding
has 51 slots, each slot containing 20 conductors. Find the
generated voltage in the machine when speed is 1500 rpm and
flux per pole is 60 mWb.
No of Poles, P = 4
No of Slots = 51
No of conductors/slot = 20
Total no. of conductors, Z = 51 × 20 = 1020
Speed, N = 1500 rpm
Flux/pole, ϕ = 60 mwb = 60 × 10 -3
No of parallel path, A = 2 (for wave wound)
Generated emf , Eg =
∅ZN P
60 A
=
60 ×10−3 ×1020 ×1500 ×4
60 ×2
=3060 V

4. The armature of a 4 pole 230 V wave wound generator has 400
conductors and runs at 400 rpm. Calculate the useful flux per pole.

5. An 8 pole lap wound generator has 1000 armature conductors, flux
per pole 20 m Wb and emf generated is 400 V, what is the speed of the
machine?

7. Separately Excited D.C. Generators
A dc generator whose field magnet winding is supplied from an
independent external d.c. source (e.g., a battery etc.) is called a
separately excited generator.
The voltage output depends upon the speed of rotation of armature and
the field current (Eg = φZNP/60 A).
The greater the speed and field current, the greater is the generated e.m.f.
Armature current, Ia = IL
Terminal voltage, V = Eg – IaRa
Electric power developed = EgIa
Power delivered to load = EgIa – I R =
= VIa

8. Self-Excited D.C. Generators
A d.c. generator whose field magnet winding is supplied current from
the output of the generator itself is called a self-excited generator.
Self-excitation is possible only if the field pole pieces have retained a
slight amount of permanent magnetism, called residual magnetism.
When the generator starts rotating, the weak residual magnetism causes a
small voltage to be generated in the armature. This small voltage applied
to the field coils causes a small field current.
Although small, this field current strengthens the magnetic field and
allows the armature to generate a higher voltage. The higher voltage
increases the field strength, and so on. This process continues until the
output voltage reaches the rated output of the generator.
Series generator
Shunt generator
Compound generator

9. DC Series Generator
In a series-wound generator, the field winding is connected in series
with armature winding so that whole armature current flows through the
field winding as well as the load.
Armature current, Ia = Ise = IL = I
Terminal voltage, V = EG – I(Ra + Rse)
Power developed in armature = EgIa
uses very low resistance field coils, which consist of a few turns
of large diameter wire. The voltage output increases as the load
circuit start drawing more current.

10. DC Shunt Generator
In a shunt generator, the field winding is connected in parallel with the
armature winding so that the terminal voltage of the generator is applied across
it.
The shunt field winding has many turns of fine wire having high resistance.
Therefore, only a part of armature current flows through shunt field winding and
the rest flows through the load.
Shunt field current, Ish = V/Rsh
Armature current, Ia = IL + Ish
Terminal voltage, V = Eg – IaRa
Power developed in armature = EgIa
Power delivered to load = VIL
Current in the field windings of a shunt-wound generator is independent of
the load current.
Since field current, and therefore field strength, is not affected by load
current, the output voltage remains more nearly constant.

11. In a series-wound generator, the output voltage varies directly with load
current. In the shunt-wound generator, the output voltage varies
inversely with load current.
A combination of the two types can overcome the disadvantages of both.
This combination of windings is called the compound wound DC
generator.
Short Shunt Compound DC Generator
shunt field winding is in parallel with
the armature winding.
Series field current, Ise = IL
Shunt field current,
Terminal voltage, V = Eg – IaRa – IseRse
Power developed in armature = EgIa
Power delivered to load = VIL

12. Series field current, Ise = Ia = IL + Ish
Shunt field current, Ish = V/Rsh
Terminal voltage, V = Eg – Ia(Ra + Rse)
The power developed in armature = EgI
Power delivered to load = VIL
shunt field winding is in parallel with both series field and armature
winding.
Long shunt Compound Generator
Compound wound generators are of two types, known as cumulative
wound and differential wound generators.
In cumulative wound generators the series field assists the shunt field,
whereas, in differential wound generators, series field opposes the shunt
field. Problems