Oscillating Curreint Circuits An Extension of the Theory of Generalized Angular

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Ann. 57, 1896; Wien, Wied. Ann. 61, 1897; Rayleigh, Theory of Sound; Braun, Phys. Za. 3, 1901; Drude, Ann. D. Phys. 13, 1904; Jones, Phil. Mag. 1907; Cohen, Bui. Bu. Stds. S, 1909; Pierce, Proc. Am. Ac. A. & Sc. 46, 1911; Fleming, Proc. Phys. Soc. 1913- t Eccles, Phys. Soc. Proc. 24, 1912. Kennelly, Proc. IRE, 1915.
The solution of this fourth degree equation is laborious, and may be avoided in the following manner. The equation may be written in the form : /hyp. Rad. X 4, and if we treat the s
...ame circuit without resistance we obtain the easily solved equation: /hyp- rad. V I -^- - ) \ sec. / The roots of this last equation will differ but little in absolute value from the absolute values of the roots of the complete equation. If (i -\-q) and (i q) are the correction factors to be applied to the absolute values of the resistanceless roots in order to obtain the absolute values of the complete roots, we may find an expression for q by means of the algebraic relations between the roots and coefficients of the above equations; and in deriving this relation the square of q may be neglected.

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