FUNDAMENTAL PROBLEMS. 67 



in the clock diagram Fig. 58. The current in the circuit is the 

 rate of change of q, that is 



Now, in Art. 24 it is shown that the rate of change of a har- 

 monically varying quantity is another harmonically varying quan- 

 tity of the same frequency, that its maximum value is o> times 

 the maximum value of the given harmonically varying quantity, 

 and that it is 90 ahead of the given harmonically varying 

 quantity in phase. That is, dqjdt ( i) is 90 ahead of q in 

 phase, and its maximum value is <*>Q(= I) as shown in Fig. 58. 



The total electromotive force required to cause the charge on 

 the condenser to vary according to equation (a) under the con- 

 ditions shown in Fig. 57, may be considered in three parts : 



1. The part required to overcome the resistance R. This 

 part is equal at each instant to Ri y and it is therefore a har- 

 monic electromotive force in phase with i t and its maximum 

 value is RL. 



2. The part required to cause the current i to increase and 

 decrease, or, in other words, the part required to overcome the 

 reaction of the inductance Z. This part is equal to L(dijdf) at 

 each instant, and it is therefore (see Art. 24) a harmonic electro- 

 motive force which is 90 ahead of i in phase, and its maximum 

 value is caZI. 



3. The part required at each instant to hold the charge q 

 on the condenser, or, in other words, the part that is required to 

 overcome the reaction of the condenser. Now, the charge q on 

 a condejiser is equal to eC y where e is the electromotive force 

 across the condenser terminals, and C is the capacity of the 

 condenser, so that e = qj C. Therefore the electromotive force 

 required to overcome the reaction of the condenser is equal to 

 qjC t that is, it is in phase with q (or 90 behind *), and its 

 maximum value is Q/C (or I/&C, since I = &>Q). 



Solution of the given problem by the clock diagram. Let the 

 line I, Fig. 59, represent the given harmonic current (the same 



