4-AJ SERIES AND PARALLEL CIRCUITS. 107 



13. For inductive reactance,* the electromotive force to over- 

 come reactance is in advance of the current by 90, as in Fig. I, 

 and is not in phase as in Fig. 5. The current lags behind the 

 electromotive force by 90, that is, the current reaches a positive 

 maximum J cycle later than the electromotive force reaches its 

 positive maximum. When R = o, tan 6 = X -=- R = oo ; #90 ; 

 power = EI cos = o. A current and electromotive force in 

 quadrature represent no power and are said to be " wattless." 



14. Theory. When a current flows in an inductive circuit, 

 the current sets up magnetic flux which is linked with the circuit. 

 When the current changes, this flux changes and a counter- 

 electromotive force is induced in the circuit tending to oppose 

 any change in the current, the current seemingly possessing 

 inertia. 



The electromotive force produced by self-induction depends 

 upon the rate of change of current,f and is 



e oc di/dt ; or, e = L di/dt. 



The negative sign indicates that the electromotive force is counter 

 to the impressed electromotive force. 



The equal and opposite impressed electromotive force to over- 

 come self-induction is 



e L di/dt. 



* ( I3a). For capacity reactance, the electromotive force to overcome 

 reactance X=i/Cw is A'/ = /-4-Cw and is 90 behind the current; the 

 current is 90 in advance of the electromotive force ; see 55. 



t ( I4a). The electromotive force produced by self-induction, expressed 

 in terms of rate of change of flux, is e = Sd<t>/dt. (Compare 33, 

 333, Exp. 5~A.) In the absence of iron, i and are proportional to each 

 other and L is constant. In this case Li = S<t>, and L = S<t>-*-i; or, the 

 inductance of a coil is equal to the flux-linkages or flux-turns S<t> for unit 

 current. Since 0QC.5Y, it follows that L<xS 2 , other things (including 

 dimensions of coil and leakage) being equal; the inductance of a coil is 

 approximately proportional to the square of the number of turns. In the 

 presence of iron, * and <t> are not proportional, and L is not constant but 

 varies with saturation. 



