The Propagation of Electric Currents in Telephone And Telegraph Conductors a C

Cover The Propagation of Electric Currents in Telephone And Telegraph Conductors a C
The Propagation of Electric Currents in Telephone And Telegraph Conductors a C
John Ambrose Fleming
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' (25) and substituting this last, (25)/in both (16) and (17), we arrive at the equations v= FjjCosh ax-Sinh ax Coth al} . . (26) i = /!{ Cosh ax- Sinh ax Tanh al} . . (27) If we reckon distances from the earthed end and let x' be such distance, so that x' = I - x, then, substituting in the above formulae, we have s' . . . "', (28) - y Smh al * = 7T -4, Cosh ax' . . . . (29) Cosh al Hence at the earthed or receiving end the current is given by i=I 1 Sechal. '. '-. . . . (30) and when I is very ...large this received current is zero.
We have then to consider the case (iii. ) When the line is earthed through a receiving instrument of knoirn resistance. We shall consider that the receiving instru- ment has a resistance /> and a negligible inductance. Then the current through the receiving instrument is /2 = 'V%/p.
L86 PEOPAGATION OF ELECTEIC CUEEENTS Eef erring to the general equations (16) and (17), v=V l Cosh ax li VBr Sinh ax, y i=Ii Cosh ax 7= Sinh ao;, we put a? = Z, and we have V 2 = I 2 p=V l Cosh al-Ii Br Sinh aZ * -(31) I^/i Cosh aZ--^=-Sinh al .


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