544 ELECTROMECHANICSCylindrical
cast-steel
shell1000-turn
coilCylindrical
plunger12.5 cm
10 cm1.25 cmg1.25 cm10 cm5 cmFigure P12.1.8Plunger magnet.BUniform vertical fieldθFigure P12.1.1012.2.2The flux-density distribution produced in a two-
pole synchronous generator by an ac-excited field
winding is
B(θ, t)=Bmsinω 1 tcosθ
Find the nature of the armature voltage induced
in anN-turn coil if the rotor (or field) rotates
atω 2 rad/s. Comment on the special case when
ω 1 =ω 2 =ω.
12.2.3The flux-density distribution in the air gap of a
60-Hz, two-pole, salient-pole machine is sinu-
soidal, having an amplitude of 0.6 T. Calculate
the instantaneous and rms values of the voltage
induced in a 150-turn coil on the armature, if the
axial length of the armature and its inner diameter
are both 100 mm.*12.2.4Consider an elementary three-phase, four-pole
alternator with a wye-connected armature wind-
ing, consisting of full-pitch concentrated coils, as
shown in Figures 12.2.3(b) and (c). Each phase
coil has three turns, and all the turns in any one
phase are connected in series. The flux per pole,
distributed sinusoidally in space, is 0.1 Wb. The
rotor is driven at 1800 r/min.
(a) Calculate the rms voltage generated in each
phase.
(b) If a voltmeter were connected across the two
line terminals, what would it read?
(c) For thea–b–cphase sequence, taket=0at
the instant when the flux linkages with the
a-phase are maximum.
(i) Express the three phase voltages as
functions of time.
(ii) Draw a corresponding phasor diagram
of these voltages with thea-phase volt-
age as reference.
(iii) Represent the line-to-line voltages on
the phasor diagram in part (ii).