314 ELECTRICAL MEASUREMENTS 



If co 2 C 2 r 2 can be neglected in comparison with unity 



Z ac = R + r + ju(L CY 2 ) approx. (8) 



If r is adjusted so that 



L = CY 2 



then 



Z ff -4- r 

 ac' **' 1^ ' 



which is the resistance of the circuit as measured by a bridge. 

 As long as the term co 2 C 2 r 2 is negligible, the compensation will 

 not be affected by the frequency. 

 As an example, consider the following data: 



L = 0.000328 henry 



R = 20 ohms 



C = 1 microfarad 



= 18.11 ohms. 



Using these values the impedances and phase displacements at 

 60 and 1,000 cycles per second are: 



Z 60 = 38.109 + ./0. 000016 



060 =0. 000024 

 Zi.ooo = 37.878 + ./0. 0265 

 0:,ooo =0.040 



If no compensation is applied the values are 



Z 60 =38.11+^0.124 

 06 =0.186 

 Zi.ooo = 38.11 + ./2.06 



a Q 1 



01,000 0.1 



To determine whether compensation is needed and to make the 

 necessary adjustments, the potential circuit is short-circuited 

 on itself and a large alternating current sent through the fixed 

 coil. 



The instrument will remain undeflected: 



1. If there be no mutual induction between the two coils. 



2. If the effective inductance of the movable-coil circuit is 

 zero, for then the currents in the movable and fixed coils will be 

 in quadrature. 



Having made sure that the mutual induction is not zero, the 

 resistance r may be adjusted until the deflection disappears. 



