PETERSEN SYSTEM OF GROUNDING 



45 



occurs when the impressed voltage to ground, E cos a7/2, is a maxi- 

 mum) : 



in = 0, 



iig + iu + iic + iic = (g'o + Co'D) ^ = 0.0173 ampere, 



gi + 22 = — Co = 0.0216 coulomb, 

 g 



The numerical quantities in the second and third of these equations 

 are respectively the total current supplied to the sound wire and the 

 total charge on this wire at the instant of breakdown. They are 

 obtained by solving the network of Fig. 3, with switch S open and 

 taking instantaneous values when the impressed e. m. f. is a maximum. 

 The resulting expressing for iig is 



iig = 0.3 X 10-«e-3i'" - 4.38 X lO-^e-^-^' cos 7300^ 

 -f 0.37 X 10-« X 37,350 cos 377/. 



The non-oscillatory term 0.3 X 10~®e~^^"*' is seen to be negligible 

 compared to the others. 



The voltage between the sound wire and ground is obtained by 

 dividing the above result by g = 0.37 X 10"^, and is 



V = 0.8e-3i« - ll,800e-«-5' cos 7,300/ + 37,350 cos 377/. 



This equation is plotted for about 13^ cycles of fundamental frequency 

 in Fig. 4. The non-oscillatory term is negligible. As will be seen, 

 the maximum overvoltage is about 30%. 



Fig. 4 — Voltage from Sound Phase to Ground Following Extinction of Arc. 



