FUNDAMENTAL PROBLEMS. 



($) Circuit containing resistance and inductance. In this case 

 the component of E parallel to / is equal to Rf, the reactance 

 of the circuit is equal to coL, and the component of E which 

 is 90 ahead of / is equal to a>LI, as shown in Fig. 60. 



V" 



Fig. 60. Fig. 61. 



this case the current lags behind E in phase by the angle whose 

 tangent is coL/R, an angle which approaches 90 when coL 

 is very large compared with R. 



(V) Circuit containing resistance and a condenser. In this case 

 the component of E parallel to / is equal to RI, the reactance 

 of the circuit is equal to minus i/coC, and the component of E 

 which is 90 behind 7 is equal to /x i/&>7as shown in Fig. 61. 

 In this case the current is ahead of E in phase by the angle 

 whose tangent is i/coC divided by R, an angle which ap- 

 proaches 90 when i /coC is very large compared with R. 



31. Growth and decay of current in an inductive circuit, (a) When a con- 

 stant electromotive force & is applied at a given instant to a circuit containing 

 resistance and inductance, the current gradually rises from its initial value of zero to 

 a final steady value equal to / R. During the time that the current is growing in 

 value, part of the impressed electromotive force acts to overcome resistance and the 

 part so used is equal to Ri ; and part of the impressed electromotive force acts to 

 cause the current to increase and the part so used is equal to L dijdt. Therefore 



we have : 



(0 



The integration of this differential equation under the condition that i = o when 

 f~o (that is i = o at the instant when the electromotive force S is applied), 

 gives the equation of the growing current, namely : 



(13) 



in which e is the Napierian base. 



