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By Tony R. Kuphaldt

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8. SOME EXAMPLES WITH AC CIRCUITS 47 must by included as additional symbols on the diagram, and there is no one ”correct” way in which to place them. They must, however, correlate with the given phase angle to represent the true phase relationship of that voltage with other voltages in the circuit. • REVIEW: • Polarity markings are sometimes given to AC voltages in circuit schematics in order to provide a frame of reference for their phase angles. 8 Some examples with AC circuits Let’s connect three AC voltage sources in series and use complex numbers to determine additive voltages.

In essence, the angled vector is taken to be the hypotenuse of a right triangle, described by the lengths of the adjacent and opposite sides. ” These two dimensional figures (horizontal and vertical) are symbolized by two numerical figures. 5. POLAR AND RECTANGULAR NOTATION 37 with a lower-case ”i” (in pure mathematics) or ”j” (in electronics). These lower-case letters do not represent a physical variable (such as instantaneous current, also symbolized by a lower-case letter ”i”), but rather are mathematical operators used to distinguish the vector’s vertical component from its horizontal component.

7. MORE ON AC ”POLARITY” 43 In AC circuits, though, we don’t deal with ”negative” quantities of voltage. Instead, we describe to what degree one voltage aids or opposes another by phase: the time-shift between two waveforms. We never describe an AC voltage as being negative in sign, because the facility of polar notation allows for vectors pointing in an opposite direction. If one AC voltage directly opposes another AC voltage, we simply say that one is 180o out of phase with the other. Still, voltage is relative between two points, and we have a choice in how we might connect a voltage-measuring instrument between those two points.

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AC by Tony R. Kuphaldt

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