by reading this below help me chart out the flow of electricity waves in its angular rate per second, since electricity is instantaneus we can only calculate its angular rate per second. since the electricity waves are instantaneous such as if we were to communicate in a chatroom every letter i type would be instantaneous, the only seemingly delay or lack of instant would be the "network" or computers inability to keep up with the signal
read this below
In the development of his expressions, by working backwards, it appears to be a “force-fit” in order to arrive at an already predetermined result, a form of contrivance to quickly reach a practical result. This obviates any understanding of the theoretical conditions involved. Steinmetz created his system of mathematics for the practicing engineer, not the theoretician. This riles the pendant, nemesis ensues.
(4) As is well known Steinmetz introduced many mathematical concepts to greatly simplify the understanding and utilization of alternating current electricity. But General Electric did not want him to put too much know how in his books. Other than Steinmetz, it was only Nikola Tesla of Westinghouse Electric that could make working A.C. equipment. But Tesla did not write books, his failing, out loss.
Thruout his writings Steinmetz utilizes a dimensionless time operator which greatly simplifies the expression of alternating current phenomena. An angular rate is substituted for a time rate. It is an instantaneous position variable along the A.C. cycle, the dimension of time is canceled by the angular frequency in radians per time, given is,
t = Time Variable, second
T = Time Period, second
F = Frequency, cycle per second
= Time Rate, per second
Hence the following expressions,
Where the factor 2pi can be called an “angular tensor”.
The differential expressions for alternating current phenomena become a dimensionless operator, not a time rate
is now,
Now it is a variation in angular position, radians are dimensionless.
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#9 (permalink)
Old 07-12-2012, 08:06 PM
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)
