INDUCTANCE AND CAPACITY 395 



In general, tan a tan b = (1 + tan a tan b) (tan (a 6)), 



so if the phase angle (p P of the standard condenser is small, as it 

 usually will be, 



tan (<p x - tpp) = wCpRp - uCxRx (29) 



Either R x or R P may be zero as previously noted. If p P is known, 

 the power factor of the unknown condenser is readily computed. 

 The values of <p P and C P would be determined by a process of 

 stepping up from an air condenser. The curves on page 361 

 were determined by this method. As it is customary to use a 

 high frequency, 800 cycles per second or greater, residual in- 

 ductances and capacities in the apparatus must be reduced to a 

 minimum. The sources of error to be considered when refined 

 measurements are to be made are: 



1. Inductance or capacity of M and N. 



2. Error in the ratio of M and N. 



3. Inductance or capacity of R x and R P . 



4. Electrostatic induction between the bridge and its 

 surroundings. 



Determination of Equivalent Capacity and Conductance of 

 Condenser or Short Length of Cable. The equivalent capacity 

 and the conductance (leakance) of a condenser, or a short length 

 of cable, may be found by means of the Wien bridge. A short 

 length of cable is specified so that the complications arising from 

 distributed capacity, inductance, resistance, and leakance may 

 be avoided, for the frequency employed is likely to be high. 



It is desired to find the combination of condenser and resistance 

 in parallel with it which will duplicate the behavior of the actual 

 condenser. No assumption is made as to the nature of the energy 

 loss taking place in the dielectric. 



The arrangement of apparatus is that shown in Fig. 230, the 

 specimen being connected in the arm X, R x being made zero. 

 CP is a perfect (air) condenser, in series with a non-inductive 

 resistance, R P , and both are adjustable. To balance the bridge 

 it is necessary to bring the current in the arms N and P into phase 

 with that in the arms M and X. This may be done, as previously 

 indicated, by putting a comparatively small resistance in series 

 with the air condenser, or by shunting that condenser with a 



