546 ELECTROMECHANICSinduced voltage, given that the number of parallel
paths is equal to the number of poles for lap
windings.
12.2.12A four-pole dc generator is lap wound with 326
armature conductors. It runs at 650 r/min on full
load, with an induced voltage of 252 V. If the
bore of the machine is 42 cm in diameter, its axial
length is 28 cm, and each pole subtends an angle
of 60°, determine the air-gap flux density. (Note
that the number of parallel paths is equal to the
number of poles for lap windings.)
12.2.13A six-pole, double-layer dc armature winding in
28 slots has five turns per coil. If the field flux
is 0.025 Wb per pole and the speed of the rotor
is 1200 r/min, find the value of the induced emf
when the winding is (a) lap connected, and (b)
wave-connected. (Note:The number of parallel
paths is equal to the number of poles for lap wind-
ings, while it is equal to 2 for wave windings.)12.2.14A four-pole, dc series motor has a lap-connected,
two-layer armature winding with a total of 400
conductors. Calculate the gross torque developed
for a flux per pole of 0.02 Wb and an armature
current of 50 A. (Note:The number of parallel
paths is equal to the number of poles for lap
windings.)
12.3.1For a balanced two-phase stator supplied by bal-
anced two-phase currents, carry out the steps
leading up to an equation such as Equation
(12.3.6) for the rotating mmf wave.
12.3.2TheN-coil windings of a three-phase, two-pole
machine are supplied with currentsia,ib,andic,
which produce mmfs given byFa=Niacosθm;
Fb =Nib cos(θm−120°); andFc = Nic
cos(θm−240°), respectively.
(a) If the three-phase windings are connected in
series and supplied by a single-phase voltage
source, find the resultant mmf due to all the
three windings as a function ofθm.
(b) If the three-phase windings are connected to
a balanced three-phase voltage supply off
Hz (with positive sequence), determine the
resultant mmf.
(c) Lettingθm=ωmt+α, obtain the relation-
ship betweenωmandω(= 2 πf )that results
in maximum mmf.
12.3.3A two-pole, three-phase synchronous generator
has a balanced three-phase winding with 15 turns
per phase. If the three-phase currents are given by
ia=100 cos 377t,ib=100 cos( 377 t−120°),
andic=100 cos( 377 t−240°), determine:
(a) The peak fundamental component of the
mmf of each winding.
(b) The resultant mmf.
12.3.4Consider the balanced three-phase alternating
currents, shown in Figure P12.3.4(a), to be flow-
ing in phasesa, b,andc,respectively, of the two-
pole stator structure shown in Figure P12.3.4(b)
with balanced three-phase windings. For instants
t=t 1 ,t 3 , andt 5 of Figure P12.3.4(a), sketch
the individual phase flux contributions and their
resultants in vectorial form.
12.4.1Consider the electromagnetic plunger shown in
Figure P12.4.1. Theλ–irelationship for the nor-
mal working range is experimentally found to be
λ=Ki^2 /^3 /(x+t), whereKis a constant. Deter-
mine the electromagnetic force on the plunger
by the application of Equations (12.4.19) and
(12.4.20). Interpret the significance of the sign
that you obtain in the force expression.tt 1 t 2 t 3 t 4 t 5ia ib ic
bca(a) (b)b'c'a'Figure P12.3.4