488 ELEMENTS OF ELECTRICAL ENGINEERING. 



give 105 volts at the middle lamp of the row. Ans. 14,040 

 circular mils sectional area. 



Note. Such problems as this and problem 157 are most easily solved on the as- 

 sumption that the given group of lamps is equivalent to a 5o-ampere load distributed 

 with ideal uniformity over the whole length of 200 feet. 



157. Find the voltage at each end lamp in the row specified in 

 problem 156. Ans. 108.85 volts at one end and 109.23 volts at 

 the other end. 



Note. The drop along ab (or cd], Fig. 164^, is equal to JfJg (^ x}dx, 



which is equal to %pXI, where pX is the resistance of ab (or cd) and I is the total 

 current delivered to the group of lamps. Compare Art. 119, Chap. IX. Therefore 

 the voltage at one end of the row is 115 volts minus the drop in (60 -f- -|fi) feet of 

 the service wire, and the voltage at the other end of the row is 115 volts minus the 

 drop in (50 -j- -\-} feet of the service wire ; with full current of 50 amperes in each 

 case. 



158. All the lamps except the middle lamp in the row speci- 

 fied in problem 1 56 are turned off. Find the rise of voltage at 

 the middle lamp. Ans. From 105 volts to 114.88 volts. 



159. Find the size of wire required to supply the row of 100 

 lamps specified in problem 1 56 by the simple parallel scheme, 

 both service wires being led from the service point to the nearer 

 end of the row : (a) when the drop between the service point 

 and the most remote lamp is 10 volts ; (^) when the drop to the 

 most remote lamp exceeds the drop to the nearest lamp by the 

 amount (109.23 105) volts ; and (r) when the drop to the most 

 remote lamp is 5 volts. Ans. (a) 16,200 circular mils sectional 

 area; (b) 25,600 circular mils ; (c) 32,400 circular mils. 



Note. In case (a] we have the same total drop as in problem 156, but the 

 voltage at the lamps ranges from 105 volts at the remote end to 111.67 volts at the 

 near end of the row, that is a range of 6.67 volts ; whereas with the return loop 

 scheme as specified in problem 156 the voltage at the lamps ranges from 105 at the 

 middle lamp to a maximum of 109.23 volts, that is, a range of only 4.23 volts, and 

 the wire in the return loop scheme is the smaller. 



In case (b} the voltage at the lamps has the same range as in problem 156 and the 

 lamps therefore would operate equally well as in the return loop scheme as specified 

 in problem 156, provided the lamps are all in use or all out of use, but the wire in 

 case (b} is nearly twice as heavy as in problem 156. This shows in a striking way 

 the saving of copper by the return loop scheme, for the same range of voltage among 



