I FFICIENCY OF ELECTRIC UKNKKATOR8. 91 



an equal amount of work. The maximum electrical Hli.-iVnry 

 occurs when the external resistance is equal to infinity ; it 

 is then equal to unity; but the capacity becomes nil, since 



E- X 4 = 0. 



The minimum efficiency, on the contrary, corresponds to an 

 external resistance equal to zero, the efficiency and the capacity 

 both becoming nil. 



In practice it is always advantageous to close a battery on 

 a comparatively great external resistance, in order to avoid the 

 development of heat, which is due not only to the current, but 

 also to certain chemical reactions, which, under the influence 

 of the temperature, quickens the dissolution of the positive 

 electrode without increasing the electrical capacity. This, 

 however, should not be pushed to an extreme, for almost every 

 battery consumes a certain quantity of material per hour in 

 either open or closed circuit, and this in excess of the quantity 

 consumed for the generation of electricity proper ; if, therefore, 

 the normal working gives only a feeble electrical capacity, the 

 efficiency may become insignificant, and the price of watts 

 expensive, notwithstanding the use of cells of great electro- 

 motive force working with economical materials. 



MAXIMUM CAPACITY OF A BATTERY COMPOSED OF A CERTAIN 

 NUMBER OF CELLS. We will suppose that a battery is composed 

 of n cells each having an electromotive force E and an in- 

 ternal resistance r, and that we intend arranging this number 



M 



of cells in p groups joined in series, each group containing - 



P 

 cells joined in multiple arc for acting on a circuit of a given 



resistance R', giving to the battery its maximum capacity. 



J)*T 



The internal resistance of the battery will be *-. The 



n 



electromotive force of the entire battery will be |?E. The 

 intensity of the current will be : 



r _ pE 



^ """ ~~o ^ o 



p r 1} P' r 



n + K 



