silsbee: inductance of resistance standards 419 



PHYSICS. — A study of the inductance of four-terminal resistance 

 standards. 1 Francis B. Silsbee, Bureau of Standards. 



The precise measurement of alternating currents frequently 

 involves the use of standard resistances, the inductance of which 

 should be known. When the currents are large the standards 

 used are usually of low resistance, and a very small inductance 

 in such a standard may produce a very considerable phase angle 

 between the voltage drop across the resistance, and the current. 

 In the range below one ohm the resistances are almost invariably 

 of the four-terminal type and, therefore, require methods of 

 measurement which are quite distinct from those applicable 

 to higher resistances. The object of this investigation was to 

 develop methods for comparing the phase angles of such four- 

 terminal resistances and also to construct standards, having a 

 very small known inductance, with which other apparatus could 

 be compared. 



If we consider a four-terminal resistance (or more briefly a 

 "shunt") which carries a sinusoidal alternating current, we will 

 find that the voltage between the potential terminals is not, 

 in general, in phase with the current, but may be resolved into 

 two components, one in phase and one in quadrature. The re- 

 sistance of the shunt is defined as the ratio of the in-phase com- 

 ponent of the voltage to the current, while the reactance is the 

 ratio of the quadrature component of the voltage to the current. 

 The angle whose tangent is the ratio of the reactance to the re- 

 sistance is the phase angle of the shunt. The inductance is, 

 of course, equal to the reactance divided by 2w times the 

 frequency; the time-constant is the ratio of the inductance to 

 the resistance. This latter quantity is very nearly constant 

 over the range of commercial frequencies and is a measure of 

 the amount by which a shunt departs from the ideal condition 

 of giving a voltage exactly in phase with the current. 



In some of the measurements described below it was neces- 

 sary to use mutual inductances, and it was found that these 

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1 Detailed paper to appear as Bur. Stds. Sci. Paper No. 281 (Bull. Bur. Stds., 

 13:375-422). 1916. 



