542 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



n=0 



This equation indicates that Vn is negative for odd numbers of arcs and 

 positive for even numbers of arcs.* If r/z is neglected, Equation 3 is re- 

 duced to 



i-iyvn = Vai - 2vn 



(3a) 



For Vai = 300 volts and y = 14 volts, the residual voltages following 

 the first four arcs are respectively —272, +244, —216 and +188. These 



Vai 



Io+iVa-L-Vj(^]'''^ 



Io+(VaL-vJ 



Zc 



t :o 



I Im 



^1 ARC TIME 



(b) 



Fig. 7 — -Mechanism of interruption of an arc. (a) Lumped circuit elements 

 (b) Distributed elements. 



values are numerically higher than measurements due to neglecting 

 the term r/z. For the circuits used in our experiments r/z ranged be- 

 tween 0.1 and 0.5 and as many as 4 or 5 consecutive arcs have been ob- 

 tained in one breakdown. Figure 8 shows a transient with both positive 

 and negative residual voltages corresponding to even and odd number 

 of arcs respectively.! 



* Except when Vn is not too much higher than the arc voltage v. 



t The following alternative explanation for the occurrence of high positive 

 residual voltage was considered : the first arc may be extinguished by the formation 

 of a metal bridge due to the arc-. This may occur before the capacitor C has at- 

 tained a negative voltage. This possibility, however, was eliminated. From the 

 measured residual voltages the energies in the arcs were calculated. The heights 

 of the bridges produced were computed (reference 2) and were found to be too 

 small compared with the contact separations. 



