PROBLEMS. 491 



the groups being 10 feet apart. The lamps are supplied with 

 current from ii5-volt mains according to the wiring scheme 

 shown in Fig. 168, Chap. IX. The end group, bb (see figure), 

 is i o feet from the mains, the point, pp, is 70 feet from the mains, 

 and No. 2 Brown and Sharpe gauge copper wire is used through- 

 out. Make a drawing like Fig. 157^, Chap. IX., showing the 

 voltage at every group of lamps. Sample answer: 1.964 volts 

 drop to the group of lamps which is 50 feet from the service 

 point. 



Note. It would be permissible for practical purposes to calculate drops to the 

 various lamps in this problem on the assumption that the lamps constitute a load 

 which is distributed with ideal uniformity. It is here intended, however, that the 

 drops be calculated as they actually are and so represented in the drawing. 



165. The core of an insulated cable is a cylindrical rod of copper | inch in diam- 

 eter, the lead sheath is i| inches inside diameter, and the space between the core 

 and the sheath is filled with rubber of which the electrical strength is, say, 120,000 

 volts per centimeter. Find the greatest voltage between sheath and core that the 

 rubber insulation can sustain. Ans. 79,130 volts. 



166. An electromotive force of 104,800 volts is applied very suddenly to two 

 parallel wires 6 mils in diameter and 6 inches apart center to center. What is the 

 diameter of fhe cylindrical region about each wire throughout which the electrical 

 stress exceeds the electrical strength of the air, namely, 26,000 volts per centimeter? 

 Ans. One-half an inch in diameter. 



Note. After the voltage has been applied and the air inside of the region one- 

 half an inch in diameter has broken down electrically, a thin cylindrical layer of air 

 at a distance of \ inch from the wire is electrically charged, and the lines of force 

 which pass outwards from this thin layer of air being in tension pull outwards on the 

 layer and cause convection currents which very quickly alter the distribution of electric 

 field between the wires. 



167. The accompanying figure, Fig. i6?P, shows two motors, 

 M and M f , two groups of glow lamps, L and L* ', and a group o^ 

 arc lamps, A, all supplied from the 1 1 5 -volt service point, P. The 

 distances are all so small that the sizes of all wires are to be de- 

 termined from the table of safe carrying capacities. The motor, 

 M, takes 35 amperes, the motor, M f , takes 18 amperes, the group, 

 L, contains 7 half-ampere lamps, the group, L f , contains 3 half- 

 ampere lamps, and each arc lamp takes 5 amperes. 



(a) Make a sketch of Fig. i6?P and indicate the values of the 

 current at the points a, b, c, d, e and f; (b) indicate the size of 



