ARCING OF CONTACTS IN TELEPHONE SWITCHING CIRCUITS 1233 



circuit during the period of rapid discharges at the contacts preceding 

 the steady arc. The analysis is based on the following simplified model of 

 the mechanism involved: (1) The first local discharge at the contact 

 takes place when the proper separation corresponding to the initial 

 voltage Vo is reached; (2) this discharge time is assumed to be short and 

 negligible in comparison to the following charging time; (3) the local 

 capacitances at the contact recharge from the main circuit until the 

 same initial voltage T^o is reached when a second discharge takes place; 



(4) this process repeats until a steady arc is established provided that 

 the circuit is capable of building up enough current, — otherwise, the 

 local discharges will continue and finally stop when the main circuit be- 

 comes incapable of charging the local contact capacitances to Vo; and 



(5) all the local discharges at the contact are terminated at a constant 

 voltage V for any one set of circuit conditions. The nature of v is left 

 to be determined and physically understood from our measurements. 



— nm^ 



CONTACTS ::=p C -iiT Vq 



Fig. 1 — Typical battery-inductance-contacts circuit. 



Battery Vo, L and Contacts, Fig. 1 



Follomng the first discharge at the contact from Vq to v the local 

 contact capacitances will recharge with a current 



/c V 

 I = {Vo — v) ij j sin 03i, 



where co = {Lc)"^'^. 



The voltage at the contact mil reach Fo at ^i = 7r/2a) and the cor- 

 responding current is 



/. = (n - -.) (if. 



A second discharge will then take place and recharging wdll proceed 

 with the new boundary conditions: at t = o, the contact voltage is v 

 and the circuit current is h. By following this procedure, a general ex- 

 pression for the nth charging process is obtained: 



I{n) = (Vo - v) (0''' inf' (a) 



