FLUCTUA TIONS IN MICROPHONES AND OTHER RESISTANCES 215 



If the value of e as given above is substituted in this equation, and 

 the relative phases of the individual contact voltages Ci • • • g„ are 

 considered random, one derives the relationship 



ei 



e2' 



^ parallel 





Rn' 



Rr^ R2^ Rx Z\ 



(6) 



The experimental test of this derived relationship will be given later. 



Assemblage with Contacts in Series 



Consider n contacts placed in series and supplied with current from 

 a battery through an inductance as shown in Fig. 13^1 . The equivalent 



^ 



(A) 



I— <3>-AM 



ei R| 



-<3D — vw 



en f^n 



(B) 



l"ig. 13 — {A) Circuit for measuring the contact noise of a series assemblage of re- 

 sistance elements. {B) The e(iuivalent a.-c. circuit of {A). 



a.-c. circuit is shown in l-'ig. 135. If the value of e- impressed on the 

 impedance Z of a measuring device is calculated, in a way similar to 

 that outlined for the case of contacts in parallel, one gets 



W + • • • ^n'']Z' 



lR,-\-R2+ ••■ Rn + ZJ • 



(7) 



Equations (6) and (7) are derived by considering the aggregate as 

 made up of single contacts, but the same would be true if the aggregate 

 were considered as made up of unit cells of arbitrary size, the values of 

 e and R applying to the unit cells. 



