108 SINGLE-PHASE CURRENTS. [Kxr. 



15. The inductance L of a circuit is defined by the foregoing 

 equations. When e is in volts and i is in amperes, L is in henries. 

 A circuit has an inductance of one henry when a change of cur- 

 rent at the rate of one ampere per second induces an electro- 

 motive force of one volt. 



1 6. When the current varies according to a sine law, 



i = /max Sin oo/. 



The impressed electromotive force is, accordingly, 



e = L di/dt = L<aI m&Ji cos wf = La>/ max sin (o>f + 90 ) . 



The impressed electromotive force to overcome self-induction 

 is, therefore, 90 in advance of the current; the current, on the 

 other hand, lags 90 behind the electromotive force. 



17. The maximum value of this electromotive force is seen 

 to be Lo> times the maximum value of the current; hence, the 

 effective value of this electromotive force is Lw times the effective 

 value of the current, that is, Ex = LtaI = XI. Fig. i and the 

 statements in 12, 13 are thus established. 



1 8. Series Circuit with Resistance and Inductive React- 

 ance. In a circuit with both R and X, the electromotive force 

 required to cause a current / to flow consists of two components, 

 which have been separately discussed in the preceding paragraphs : 

 RIj in phase with /, to overcome resistance; 

 XI, 90 ahead of /, to overcome reactance. 



Thus in Fig. 2, if OD is current, OC is the electromotive force 

 to overcome resistance and CA is the electromotive force to over- 

 come* reactance, OA being the total impressed electromotive 

 force. These electromotive force relations are fundamental and 



* ( i8a). These electromotive forces, CA and OC are components of 

 the impressed electromotive force. In the opposite sense, as counter- 

 electromotive forces, we have the counter-electromotive force AC, lagging 

 90 behind the current, produced by inductive reactance ; and, the counter- 

 electromotive force CO, opposite in phase to the current, produced by 

 resistance. Compare 15, Exp. 6-A. 



