FUNDAMENTAL PROBLEMS. 87 



desirable, and in some cases feasible, to reduce this backward 

 flow of energy by connecting a condenser or something which is 

 equivalent to a condenser (such as an over-excited synchronous 

 motor) in parallel with the receiving circuit. 



Let OE, Fig. 82, represent the voltage at the terminals of the 



'f 







Fig. 82. 



receiving circuit, and let 01 represent the current delivered to the 

 receiving circuit. Let R be the resistance of the receiving circuit 

 and X its reactance. Then 



and 



sin0 



l/R 2 + X* 



The component Ob of the current / is equal to /sin 6 or 

 But / is equal to E/l/R^+X 2 , so that the 



component Ob is equal to EX/(R 2 + X 2 ). If a condenser of 

 capacity C is connected across the transmission line at the 

 receiver end, then the current flowing into the condenser will be 

 90 ahead of E, or parallel to Oc, Fig. 82, and its value will be 

 equal to E divided by the condenser reactance i/<*>C, or to 

 EcoC; and if this current is numerically equal to Ob, the sum 

 of / and Oc will be in phase with E. That is, the receiving 

 circuit and the condenser together will take current in phase with 

 E, and the instantaneous value of power delivered over the trans- 

 mission line will never be negative. The capacity of the con- 

 denser required to produce this result is given by the relation 

 above mentioned, namely, EcoC= EX/(R 2 -f X 2 ), which gives 



c- x 



