76 Conductors and Condensers 



and the total charge E is given by 



E = e l + e^ + . . . 



[OH. m 



Thus the system of condensers behaves like a single condenser of capacity 



It will be noticed that the compound condenser discussed in 81 con- 

 sisted virtually of two simple spherical condensers connected in parallel. 



Condensers in Cascade. 



86. We might, however, connect the low potential plate of the first to 

 the high potential plate of the second, the low potential plate of the second 

 to the high potential plate of the third, and so on. This is known as 

 arranging the condensers in cascade. 



FIG. 32. 



Suppose that the high potential plate of the first has a charge e. This 

 induces a charge e on the low potential plate, and since this plate together 

 with the high potential plate of the second condenser now form a single 

 insulated conductor, there must be a charge + e on the high potential plate 

 of the second condenser. This induces a charge e on the low potential 

 plate of this condenser, and so on indefinitely; each high potential plate will 

 have a charge + e, each low potential plate a charge e. 



Thus the difference of potential of the two plates of the first condenser 

 will be e/C lt that of the second condenser will be e/C 2 and so on, so that the 

 total fall of potential from the high potential plate of the first to the low 

 potential plate of the last will be 



1 1 



We see that the arrangement acts like a single condenser of capacity 



1 

 1 1 



