34^ ELEMENTS OF ELECTRICAL ENGINEERING. 



motive force E l to a receiving circuit of which the power factor, 

 cos 6, is given ; the line drop, frequency, length of line, and dis- 

 tance apart of wires being given. 



The generator voltage E Q is equal to the sum (numerical sum) 

 of EI and line drop. 



The full load current / is found from the relation E^I cos 6 

 equals P. 



The component of E l parallel to / is E l cos 0, and the 

 component of E l perpendicular to / is E v sin 6. 



By treating the problem first as a direct-current problem, the 

 approximate resistance r' of the line is found from the relation 

 r' I equals line drop. From this approximate resistance and the 

 known length of the line, the approximate size of the wire and the 

 line reactance x may be found from the table ; and since the line 

 reactance varies but little with the size of the wire, the value of x 

 need not be further approximated. 



The component of E parallel to / is E l cos -f- rl, where r 

 is the true resistance of the line, and the component of E Q perpen- 

 dicular to / is E! sin 6 + xl. Therefore 



E* = (E^ cos e + rlj + (E l sin 6 + xlj 

 or 



2 (E l sin + xlj -- E l cos ... 



From this equation the true line resistance r may be found 

 and thence the correct size of wire. 

 Example : 



E l = 20,000 volts. 



P= i, ooo kilowatts. 



cos = 0.85 = power factor of receiving circuit. 



E Q = 23,000 volts, or line drop = 3,000 volts. 



frequency = 60 cycles per second. 



distance = 30 miles. 



distance apart of wires = 1 8 inches. 



