POWER AND POWER-FACTOR. 71 



If it is decided to use a type of coil having a core 

 with an iron section of 3 sq. in., and the maximum 

 induction to be employed is 30,000 lines per square inch, 

 the value of Z = 3 x 30,000 = 90,000. 



Hence the number of turns of wire must be 

 37,000,000 _ 

 90,000 



Resultant of Two Currents Not in Phase. Exactly as with 

 an alternating electromotive force, an alternating -current 

 may be looked upon as the sum of two component 

 currents. In this case the instantaneous value of the 

 total current is at any moment the sum of the instan- 

 taneous values of the two component currents. 



Also, if represented on a vector diagram, the line 

 representing the total current is the diagonal of the 

 parallelogram having the component currents as sides 

 drawn to scale and correct difference of phase. 



A case in which currents differing in phase and 

 magnitude are combined together occurs when a circuit 

 divides into two branches of unequal resistance and 

 inductiveness, these branches again uniting to form the 

 main circuit. Thus in Fig. 32 two circuits of this kind 

 lie between the points X and Y. Between X and Y is an 

 alternating voltage. One branch circuit is non-inductive, 

 and consequently the current in this branch is in phase 

 with the voltage maintained between X and Y. The 

 other branch is, however, partly inductive, and the current 

 lags behind the voltage in phase. 



Thus in the two branch circuits there are two currents 

 differing in phase and in magnitude, but the resultant 

 current flowing from X to Y must be the same as flows in 

 the single conductor forming the remainder of the 

 circuit. On account of the difference in phase between the 

 two currents, the sum of the currents measured in each cir- 

 cuit separately will not be equal to the total current. They 

 must be combined in exactly the same manner as two 

 electromotive forces which are not in phase. 



The composition of currents in this way is best 

 illustrated by the following experiment, in which the 

 currents first flow in two branch circuits, where they are 

 measured separately, and are then made to flow together 

 through a single conductor where the resultant current is 

 measured. 



