4-A] 



SERIES AND PARALLEL CIRCUITS. 



117 



Here R 2 is the resistance of the coil, as measured by direct 

 current. The inductance, in henries, is L 2 = X 2 -f- 27rw. 



For the accurate determination of L by either of these methods, 

 the wave form of electromotive force should be sinusoidal and 

 the losses in instruments should be taken into consideration, 23a. 



48. (c) Resistance and Coil in Series. In a series circuit 

 there is one current which is the same in all parts of the circuit ; 

 electromotive forces are added vectorially, i. e., the voltage drops 

 around the separate parts of the circuit, when added as vectors, 

 give the total impressed electromotive force of -the circuit. 



FIG. 8. 



O / D 



Resistance and coil in series. 



The three readings of the voltmeter, E, E and E 2 , are, accord- 

 ingly, drawn to scale so as to form the triangle OAB, in Fig. 9. 

 The current I is laid off in phase with E lf since the current and 

 electromotive force in the non-inductive resistance are in the same 

 phase. OCA is then drawn as a right triangle. 



We have then the in-phase electromotive forces, OB = RJ to 

 overcome the resistance R lf and BC = R 2 I to overcome the resist- 

 ance R 2 ; and the quadrature electromotive force, CA = L 2 wf 

 = X 2 I, to overcome the reactance X 2 . It will be seen that Fig. 9 

 is the same as Figs. 5 and 7 combined in one diagram so drawn 

 that the current in both parts of the circuit is the same in magni- 

 tude and in phase. 



49. Three-voltmeter Method. The foregoing construction, 

 known as the three-voltmeter method, enables us to calculate L 2 





