KENNELLY. — EQUIVALENT CIRCUITS OF COMPOSITE LINES. 37 



Equivalent Circuits of Single Line. 



The equivalent T of this lino is a star-connection of three resist- 

 ances AO, GO, BO (Figure 2), two of which — the line-branches AO, OB, 

 — are equal ; while OG is a leak- 

 age-resistance to ground. This 

 equivalent T, when correctly pro- 

 portioned, has the property of «■ T . ..,« .„.» ■ . .._ .._»• B 

 being able to replace the uni- 

 formly leaky line AB, without 

 disturbing in any manner the 

 system of potentials and currents 

 outside the terminals ABG. Let 

 g' = l/R' be the conductance of 

 the leak OG' ; then 



g' = y sinh 6 mhos, (17) 



where y = l/z mhos, the recipro- 

 cal of the surge-resistance. We 

 may call y the surge-conductance 

 (A. C. surge-admittance). 



Figure 2. Equivalent T of uniform 

 line. 



Let p be the resistance of each line-branch AO, OB ; then 



= z tanh 5 = 2 



>"=36Z6-86 



II 



On 



to 



X 



ll~ 



ON 

 B 



Z'JSIZOSxIQ' 



Or' 



Figure 



and 



Equivalent n of uniform 

 line. 



coth 6 - R' = R f - R' mhos. (18) 



Thus, for the line above con- 

 > B sidered, g' = 0.001 X sinh 2 = 

 0.001 X 3.62686 = 3.62686 X 

 10" 3 mho ; while R' = \/g r = 

 275.7205 ohms. P ' = 1000 coth 2 

 — 275.7205 = 761.594 ohms. 



The equivalent l~l of the line 

 is a delta-connection of three 

 resistances AB, AG", BG" 

 (Figure 3), the two " pillars " or 

 leaks AG", BG", being equal 

 Gr conductances of g" mhos each, 

 and the "architrave " AB being 

 the line-resistance p". 



= z sinh 6 

 d 



2 



= G a 



p 

 = l/R" = y tanh 



= y coth — yl 



ohms (19) 

 mhos 

 mhos, (20) 



