MEASUREMENT OF INDUCTANCE 377 



inductance, and these advantages make this bridge superior to practi- 

 cally all other bridges for this type of comparison. 



This paper contains a discussion of the theoretical relations of this 

 bridge circuit, its possibilities and limitations for the accurate measure- 

 ment of inductance and effective resistance, and the sources of error 

 and methods of eliminating them. A shielded bridge, constructed 

 for use in calibrating inductance standards, is described and sufficient 

 measurements are given to show the accuracy of which it is capable. 



The maximum frequency at which measurements were given by 

 Owen is 530 cycles. For the measurement of telephone apparatus 

 considerably higher frequencies are used, and it is desirable that the 

 bridge be capable of measurements up to 3,000 cycles without loss 

 of accuracy. It is in the upper part of this range that the greatest 

 difficulties are encountered, requiring special precautions not so 

 necessary for the lower frequency measurements. 



While in the following discussion the maximum frequency considered 

 is 3,000 cycles, this is not meant to indicate a maximum limit to this 

 type of bridge. 



Equations of Balance 



Taking into consideration the phase angle of the resistances and 

 the loss in the condensers, the complete network is shown in Fig. 1, 

 the reactive component of the resistances being shown as series 

 inductance, and the condenser losses as series resistance. Let 



L and Re = Inductance and effective resistance of coil to be measured, 

 ri and h = Total resistance and inductance in arm BC, 

 r-> and h = Resistance and inductance in CD exclusive of R^ and L, 

 R dwd li = Total resistance and inductance in ^D including the 

 equivalent series resistance of d, 

 fs = Equivalent series resistance of C3. 



The inductance in the arm AB may readily be reduced to a negligible 

 amount and will not be considered. 



We may now balance the bridge with the inductance terminals 

 short circuited, that is, take a zero reading, and then balance again 

 with the inductance inserted. 



Writing the equations of balance in each case, subtracting one from 

 the other, and separating reals from imaginaries, we get the following 

 equations: 



C-MR - R') = L -\- ik - /./) + C,r,(r, + R^ - r/) 



