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Theory and Calculation of Alternating Current Phenomena by Charles Proteus Steinmetz

By Charles Proteus Steinmetz

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Ir, s'ented by OE line induces r in the diagram. F. which / and reactance is The self-inductance of the proportional to the current x, and lags a quarter of a period, or 90,, behind the current. F, AL TERNA TING-CURRENT PHENOMENA. F. F. in phase, X OE . F. 90 ahead of the current. F. , E, Er and Ex hence it is determined as their resultant. F. F. F. we the generator side of the line, to yield the at the receiving end of the line. Algebraically, at E get from Fig. 12 E = or, In this instance .

The 7X . N sin 2 TT (t tj, is called the funthe further terms are harmonic; first called the higher harmonics, or "overtones," in analogy to the overtones of sound waves. }\Q N th harmonic. By / /j, resolving the sine functions of the time differences, t /2 we reduce the general expression of . . , the wave to the form i = ^i + sin 2 l irNt -f cos 2 -xNt ^ 2 +A /7g. 2. The two : sin 4 cos 4 TT^V? +A ^ vNt + z sin 6 TrTV7? + . . 8 cos 6 irNt +. . Wave without Even Harmonics. half-waves of each period, the positive and the negative wave (counting wave in a definite direction in Hence the even almost always identical.

The resultant of all the currents flowing towards a GRAPHIC REPRESENTA TION. 17] distributing point, as found waves, 23 by the parallelogram of sine is zero. , or IE cos Suppose, as an instance, that over a line having the = where resistance, r, and the reactance, x QirNL, 17. F. of E 12. Fig. What volts. F. required at the generator ? In the polar diagram, Fig. F. , E, at the end of the a vector, OE. , Ir, s'ented by OE line induces r in the diagram. F. which / and reactance is The self-inductance of the proportional to the current x, and lags a quarter of a period, or 90,, behind the current.

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