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On some resistance properties of a certain network containing inductances and capacities and their analogies in a vibrating mechanical system

Published online by Cambridge University Press:  24 October 2008

E. B. Moullin
E. B. Moullin
Affiliation:
Downing College
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Extract

In the network shown diagrammatically in Fig. 1, A0A3, A3A5,… are resistances of values a1, a3,… joined in series with one another, and A3B3, A5B5,…are resistances of values 1/a2, 1/a4,…: the points B0B3,… are all on a cable of negligible resistance. The members A0A3, A3A5,… will be called the series members of the network, and the members A3B3, A5B5,… will be called the shunt members of the network: the points A0B0, will be called the input terminals of the network. If a potential difference is maintained between the input terminals, currents will flow in the members of the network.

Type
Articles
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 23 , Issue 4 , October 1926 , pp. 391 - 402
Copyright
Copyright © Cambridge Philosophical Society 1926

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References

* Though both Xr and Yr become infinite at a certain frequency, it may be shown that their sum cannot be zero. Both Xr and Yr consist of two parallel branches, one whose impedance is positive and increasing and the other whose impedance is negative and decreasing for a steady increase of frequency: hence the rate of change of each branch impedance is positive. From this it follows that Xr/Yr cannot have the value −1.Google Scholar