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Q. emf produced by windings?
The time variation of emf for a single conductor corresponds to the spatial variation of air-gap flux density. By suitable winding design, the harmonics can be reduced appreciably, and the waveform of the generated emf can be made to approach a pure sine shape.
Figure shows an elementary single-phase, two-pole synchronous machine. In almost all cases, the armature winding of a synchronous machine is on the stator and the field winding is on the rotor, because it is constructionally advantageous to have the low-power field winding on the rotating member. The field winding is excited by direct current, which is supplied by a dc source connected to carbon brushes bearing on slip rings (or collector rings). The armature windings, though distributed in the slots around the inner periphery of the stator in an actual machine, are shown in Figure (a) for simplicity as consisting of a single coil of N turns, indicated in cross section by the two sides a and -a placed in diametrically opposite narrow slots. The conductors forming these coil sides are placed inslots parallel to the machine shaft and connected in series by means of the end connections.
The coil in Figure (a) spans 180° (or a complete pole pitch, which is the peripheral distance from the centerline of a north pole to the centerline of an adjacent south pole) and is hence known as a full-pitch coil. For simplicity and convenience, Figure (a) shows only a two-pole synchronous machine with salient-pole construction; the flux paths are shown by dashed lines. Figure (b) illustrates a nonsalient-pole or cylindrical-rotor construction. The stator winding details are not shown and the flux paths are indicated by dashed lines.
Q. The energy stored in a 2-µH inductor is given by w L (t) = 9e -2t µJ for t ≥ 0. Find the inductor current and voltage at t = 1 s.
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