682 INDUSTRIAL APPLICATIONS. 



1241. ON VOLTAIC BATTERIES. In an ordinary battery, the 

 energy is withdrawn from the work of chemical action. Let us 

 suppose that the battery consists of N identical couples, associated 

 in q parallel series of n elements each ; let e be the electromotive 



force and r the resistance of each element ; the electromotive force 



nr 

 of the battery is E = ne, and its internal resistance R = . 



*. If the intensity of the current is I, the work done by the 

 chemical action in each unit of time is 



W = EI, 



and the external utilisable work 



U = EI-R P = EI/ I -^ 

 V E 



the efficiency u is then 



w = U = i _R I 



If I = is the intensity of the current corresponding to an 



RO 

 external work null, the expressions for U and u become 



The external work U first increases, and then diminishes, when 

 the current diminishes, starting from its maximum value I to zero ; 

 the efficiency, on the contrary, always increases in the same con- 

 ditions, and tends to unity, as the useful work tends towards zero. 



The sum of the two factors I and I - 1 being constant, the 

 external work attains its maximum value U m for the condition 

 I = 2l. The efficiency is then equal to 0-50, and we have 



RoIJ E 2 * ^ 6* 



^m=--=^= n q = N . 



4 4 R 4 r ^r 



