The Measurement of Capacitance in Terms of Resis- 

 tance and Frequency 



By J. G. FERGUSON and B. W. BARTLETT 



Synopsis: The adaptation of a bridge circuit due to M. Wien together 

 with apparatus and procedure is described which permits measurement of 

 capacitance in terms of resistance and frequency with an accuracy com- 

 parable to that of the primary standards. Among its advantages over the 

 Maxwell method commonly employed are the use of a single frequency 

 voltage and the fact that there is no general limitation placed on the type 

 of condenser which may be measured or on the frequency at which the 

 measurement may be made. The method is also applicable to the deter- 

 mination of inductance since its unit, like that of capacitance, may be 

 derived from the units of resistance and frequency. 



Introduction 



CONDENSERS are commonly measured by comparison with 

 standard condensers of known value by means of one or another 

 of the well-known bridge methods. The accuracy with which such 

 measurements can be made depends upon the accuracy with which the 

 capacitance of the standard is known. 



The unit of capacitance is derivable from those of resistance and 

 frequency and to obtain an absolute value for a standard of capacitance, 

 some method is required for a precise determination of capacitance in 

 terms of frequency and resistance. Of the methods which have been 

 proposed, few yield the accuracy with which the primary standards of 

 resistance and frequency are known and reproducible. 



A generally accepted method for the absolute determination of 

 capacitance in terms of resistance and frequency is to use a bridge, due 

 to Maxwell,^ employing the alternate charge and discharge of a con- 

 denser. This method has been used successfully by the Bureau of 

 Standards,^ which has obtained results of high accuracy. Several 

 fundamental limitations, however, make it difficult for general use. 

 Because of the operation of charge and discharge it is only applicable 

 to the measurement of capacitances which are independent of fre- 

 quency.^ Practically this limits the method to the measurement of 

 air condensers, which in large sizes are not very stable. Moreover 

 the balance depends on the integration of successive charges and dis- 

 charges of a condenser through a galvanometer and great care is re- 

 quired to insure that the galvanometer integrates correctly. 



1 J. Clark Maxwell, "Electricity and Magnetism," second edition. Volume 2, 

 pp. 776-7. 



2 E. B. Rosa and N. E. Dorsey, Bureau of Standards Bulletin, Vol. 1, p. 153. 

 ^ H. L. Curtis, Bureau of Standards Bulletin, Vol. 6, 1910, p. 433. 



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