42 BELL SYSTEM TECHNICAL JOURNAL 



arc. Following its extinction, there is a further action of the resonant 

 system consisting of the coil and the total capacity to ground which 

 acts in such a way as to prevent any over-voltage and to restore the 

 normal potentials to ground gradually, thus tending to prevent the 

 arc from restriking. This action is as follows: 



Fig. 2 — Vector Diagram Showing Relations of Voltages and Currents at and Follow- 

 ing Extinction of Arc 



Referring to Fig. 2, the vectors £io, -E20, -E30 represent the emfs. 

 impressed between lines and neutral by the transformer bank. 7^, 

 /„, If are respectively the admittance current to the fault, the current 

 supplied by the reactor to the fault, and the total fault current. The 

 fault is assumed to be on phase 3. The arc will go out when If passes 

 through zero. At this instant, £30 is also zero and /„ and 7^ have 

 nearly their maximum values. Their instantaneous values are, how- 

 ever, exactly equal and opposite in the sense indicated by the arrows 

 in Fig. 1, i.e., regarded as currents fed to the fault by the two parallel 

 circuits (1) coil-fault-faulty wire-Eso and (2) admittance of sound 

 phases-fault-faulty wire-transformer bank. These instantaneous 

 currents are exactly equal in magnitude and are in the same direction 

 in the single series circuit consisting of coil, transformers, admittance 

 to ground of the three phases in parallel, and ground. Thus the 

 condition in this series resonant circuit at the instant of extinction 

 is that of an established free oscillation, the energy of the oscillation 

 being at this instant wholly electromagnetic. 



The voltage across the reactor due to the current 7„, in the direction 

 of £30 (Fig. 1) is represented in Fig. 2 by the vector £og- This is 

 180° out of phase with E30 and initially of the same amplitude. At 

 the instant the arc goes out, both are practically zero. As the oscilla- 

 tion progresses, Eq^ dies away, due to damping, and the resultant 



