58 Kansas Academy of Science. 



be found by a method similar to that used in finding the resistance 

 of a divided circuit: 



. 1 _ 1 ^ 1 ^ Xi-jRi 

 Zi Ri jXi RiXi 



Xi =— — , C being the unknown capacity of the condenser and W 



the angular velocity of a single rotating coil making the same 

 number of alternations per second as the alternating currents used, 

 and therefore equals 2- times the frequency of the current used. 



T? X 



From the above equation Zi = . Also Z2 = R2, Z3 = R3, 



Xi-jRi 



and Z4 = R4 — jXi. 



When the bridge is balanced for alternating currents these im- 

 pedances are proportional: 



.■- Zi : Z-2 = Zi3 : Z4 or Zi Z4=:Z2 Z3 



.-. ^'^' (R4-jX4)=R2 Rs 



'■' Xi Ri R4 — jRi Xi X4 = R2 R3 Xi — jRi R2 R3 



This equation contains both real and imaginary quantities, and 

 therefore the real quantities must be equal to each other, and the 

 same for the imaginaries: 



.'. Xi Ri R4 = Xi R2 R3 and Ri Xi X4 = Ri R2 Rs 



.-. Ri R4 = R2 Rs and Xi X4 = R2 R3 



The first was obtained before on balancing the bridge for direct 



currents. From the second equation, Xi=^ — - 



X4 



Since K is a self-inductance, X4 = L^ 



1 R2 R3 1 r^ i-t 



and C = 



C^v L/^ R2 R3 



In this experiment a variable known self-inductance was used 

 at K, and it balanced the bridge at 20.5 rail-henrys. The values of 

 the resistances used were Ri = R3 = 400 ohms, R2=:R4 = 52.66 ohms. 

 The results are better when the values of the resistances are so 

 chosen that the resistances of the two branches between D and E 

 are nearly the same. 



0205 



For these values C = '- =.973 microfarads. 



(52.66) 400 



