SLO\\" HKLKASK ItELAY DESIGN 207 





catod in V\ix.. 12(a). 'I'luis tlic total conductance Gs is given by: 



{dr 



JTTpr 



wlicrc p is the ivsistixity of the nialerial. On integration, there is ob- 

 tained: 



Gs= -^ In -^ . (19) 



The vahie of p for copper is 1.73 X 10 ' ohm-cm. If r-y is twice Vi , for 

 example, and f = o cm, the value of Gs given by (19) for a copper sleeve 

 is 320,000 mhos. 



In the case of a sleeve of rectangular section, as shown in Fig. 12(b), 

 an approximation may be obtained by taking the sleeve as made up of 

 sliells with straight sides parallel to the center hole, connected by quarter 

 circles. Then the perimeter of the shell at a distance r from the center 

 hole is 2(6 + f/ + xr). The total sleeve conductance is therefore given 

 l)v: 



Gs = r 



Jo 



2(6 + d + 7rr)p 



in which /-o is the wall thickness. On integration, there is obtained the 

 equation : 



G, = JL i„ ('i+r'L+in) . (20) 



27rp \ -\- d I 



This expression is identical with that for the cylindrical sleeve, as 

 given by (19), when the ratio ro/ri of the radii is ec^ual to the ratio of 



(6 + rf + xa) to (6 + d). 



Coil Conductance 



For a cylindrical coil, the number of turns N is determined by the 

 area of the coil section cut by a plane through the axis, or {(r-i — ri), 

 where ( is the length of the coil and /'i and r-j, are its inner and outer 

 radii. If a is the cross sectional area of the wire, and e the fraction of the 

 coil space occupied b}' the conductor, 



Na = e({r.2 - n) . 



The mean length of turn is x(r2 + n), and the total length of conductor 

 is .V times this. Hence the resistance R is given by: 



