86 ELEMENTS OF ELECTRICAL ENGINEERING. 



between the values of E l and E Q is the required transmission line 

 drop. 



The value of yV 2 / 2 -f x^P is called the impedance drop, and 

 the difference between the numerical values of E Q and E l is 

 called simply the (voltage) drop in the line. 



40. Circuits in parallel. The general problem of circuits in 

 parallel is discussed in Chapter V. Two simple cases of this 

 problem are, however, of sufficient interest to be treated in this 

 chapter on fundamental problems, namely, (a) the problem of 

 finding the power factor of two receiving circuits in parallel, the 

 power factor of each and the current delivered to each being 

 given, and (fr) the problem of compensating for lagging currents. 

 (a) Power factor of receiving circuits in parallel. Let the line 

 OE, Fig. 8 1, represent the voltage across the two receiving 



circuits. Let /, be the 

 current delivered to re- 

 ceiving circuit number i 

 and cos l its power factor, 

 and let / 2 be the current 

 delivered to receiving 

 circuit number 2 and cos 

 2 its power factor. Lay 

 off the clock diagram in 

 Fig. 8 1 carefully to scale, 

 and draw the diagonal / as shown. The angle 6 between E 

 and / is then the angle whose cosine is the required power 

 factor of the two receiving circuits in parallel. 



(fr) Compensation for lagging currents. When a transmission 

 line delivers current to an inductive receiving circuit, power is 

 delivered over the line to the receiving circuit during the time 

 that the product ei is positive, and power is delivered back over 

 the line from the receiving circuit to the generator during the time 

 that the product ei is negative (compare Art. 9). This backward 

 flow of energy from receiving circuit to generator represents an 

 essentially unnecessary service of the transmission line, and it is 



