Thread: Eric Dollard
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Old 07-12-2012, 08:06 PM
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Law of Electro-Magnetic Induction, Three (2 of 2)

(5) Thru this methodology the A.C. wave is simplified in expression, its frequency is of unit value. This is a consequence of the fact that all parts of an alternating current networks are all operating at the exact same frequency, differing only in their angular position along the unit A.C. wave. For example, at a frequency of 60 cycles per second







Hence for 60 cycles the angular position is given by



For one radian it is that



This the time taken for the 60 cycle A.C. wave to advance one radian in its angular progress thru a cycle. This is a dimensionless operation. This angular position variable is like an instantaneous versor operator of infinitesimal unit positions. This operator is then compounded with the quadrantal A.C. operator,



Where is given by









The result is the segregation of the resistive from reactive terms, or more properly the kilowatts from the kilovolt-amperes reactive. Great simplification is derived here thru inductance expressed in ohms as is resistance, and by capacitance expressed in siemens as in conductance. The differential expressions vanish and Ohm's Law as well as Kirchoff's Law can be utilized in alternating current circuits. This is known as the “Steinmetz Method” a mathematical breakthru for the expression of the phenomena of alternating electric waves. This was the birth of electrical engineering in alternating current systems. While the engineer loves it, (This is why E.F.W. Alexanderson came to America, in order to work with the great engineering mathematician, Dr. Steinmetz.) the pendant has a deep contempt for the Steinmetz methodology (Pupin). At a common level, upon my unusually high test scores in naval electronics entry school, this thru my use of the Steinmetz method, naval instructors accused me of cheating, and caused me trouble!

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