Chap. 10] 



ELECTRICAL METHODS 



753 



In a modification of the original ratiometer, the I.G.E.S. used con- 

 densers in parallel with the resistances. Then the admittance 1/Z in each 

 arm is 





1 



= ^+i2,r/C. 



j2^fC 



li 1/R = g, the conductance and 27r/C = h, the capacitative susceptance 

 of the circuit, then the admittance is g + jh, and the ratio is 



Vi 



gi + jhi 

 g2+ jhz* 



(10H136) 



:::^: 



^MA/W 



500u 



.mjifd 





I; 



"Af^^W 



XXfa) 



In the parallel ratio-arm instrument (see Fig. 10-81) the variable capaci- 

 ties and resistances are so graduated that the conductances gi and g2 and 

 the susceptances hi and hz are in the same units, 

 the unit being the conductance of a 300,000 ohm 

 resistance. When the frequency is 535 cycles per 

 second, this is approximately equal to the suscept- 

 ance of a condenser of a 0.001 microfarad 

 capacity, and the various portions of the variable 

 capacity come out as whole numbers. 



In the Swedish-American Racom (ratio com- 

 pensator) bridge, inductive reactances take the 

 place of the capacitive reactances; phase differ- 

 ences are not read but merely compensated by 

 the use of a variable mutual inductance. A 

 schematic circuit diagram is given in Fig. 10-82. 

 The P.D.R., as computed from the resistance 

 ratio, represents the ratio of the in-phase com- 

 ponents of the potential drops. With Ra and Rb 

 as contact resistances of the stakes A and B, and Rl^ 

 resistances of coils La and Lb , the ratio is (approximately) 



T TTT 



^ 



Fig. 10-81. Parallel ca- 

 pacity ratiometer (after 

 Edge and Laby). 



and Rlb as 



Vac _ Ra -^ Rla + Ri 

 VcB Rz + Rlb + Rb 



(10-44a) 



The contact resistances may be determined and eliminated by a second 

 setting of the resistances Ri and ^2 • Then 



Vac 



VcB 



Ra + Rla + ^1 

 R2 + Rlb + Rb 



Hence, by combination, 



Vac 

 Vbc 



Ri — Ri 

 R2 — R2 



(10^46) 



(10^4c) 



