so BELL SYSTEM TECHNICAL JOURNAL 



the three direct capacities to ground are the same. The equation is 

 equivalent to 



3 1 + Zr^Y' 



where E^^ is the " characteristic residual voltage " ® of the (isolated) 

 system and is equal in magnitude to 3 £oi times the ratio of the residual 

 admittance to ground to the total admittance to ground. 

 We have 



YZ„ = Yng - Oi'^LnC + > (Cr„ + Lng) 



r„ and L„ being the resistance and inductance of the earth coil, and 

 g and C the total leakance and capacity to ground, respectively. 

 Also, for resonance 



c^^LnC = 1 



and hence the above expression for !„ becomes (at fundamental 

 frequency) 



In = 



r 



- — + i r — + — 1 



if the earth coil is adjusted for accurate resonance. 



If in this equation the denominator on the right be denoted by x 

 and the fractional unbalance of the admittance to ground by y 



( . Fi + F2gi^="'° + F3ei24o°\ 

 y-e., y = y I , then 



/. = ^^^ (3) 



X 



and, Vn being voltage between neutral and ground, 



Vn = ZJn 

 X 



If the losses in the system (including the earth coil) are small, x is 

 small compared to 1. Thus we get, for the absolute value of V 



I V„\ = 1 - . £oi 1, approximately 



and the absolute value of the residual voltage is three times this, 

 approximately. 



• Ibid., p. 257. 



