ELECTROSTATICS 27 



and, therefore, the capacity of the system consisting of three con- 

 densers in series is 



c = l = i r T ...... (50) 



Ci Cz Cz 



When two equal condensers of capacity C are connected in 

 series, their joint capacity is 



2' 



(51) 



and is equal to one half of the capacity of either condenser alone. 



24. Energy Stored in a Condenser. When a condenser is 

 being charged, work is uC ne m ra i sm S the charge through the 

 difference of potentia\ V^ the terminals, and this amount of 

 energy is stored in the elect,^ atic field of the condenser. 



In Fig. 22 PN is a condenser of capacity C formed of two 

 parallel plates separated by t cm. of a dielectric of constant K. 

 When a potential difference e is produced between the plates by 

 the generator G, electricity flows from N to P until the charge 

 on P is 



q = Ce; 



if the potential e is increased by de the charge q is increased by 

 dq = C de and the work done in raising the charge dq through the 

 difference of potential e is 



dco = e dq = Ce de. 



The total work done in charging the condenser with a quantity 

 of electricity Q, or to a difference of potential E, is 



W 



-c\ e 



.2 

 = cjergs (52) 



Thus the work done in charging a condenser, or the energy 

 stored in the electrostatic field of the condenser, is equal to one 

 half of the capacity multiplied by the square of the difference of 

 potential between the terminals. 



