MEASUREMENT OF INDUCTANCE 379 



L = CMR -R'), ' (6) 



the percentage error due to neglecting h — h' being 



100(/2 - y) (J. 



From equation (5), the effective resistance of L is giv^en by 



Re = r./ - r,, . (8) 



the percentage error due to neglecting corrections being 



Qi + ^i + w ]• (9) 



Re V ' ^^ ' <2: 



The error In L is approximately, from equations (7) and (8), 



X2 — X-/ Re _q2 



Re ' X ~ Q' 



where q-2 = ratio of reactance to resistance of change in arm CD, and 

 Q = ratio of reactance to resistance of the inductance being 

 measured. 



This error is usually negligible and may be approximately corrected 

 for when appreciable. Dr. Owen has pointed out that this type of 

 error is not peculiar to the Owen bridge, but is present in practically 

 all methods of inductance measurement. 



The error in Re is a function of the Q of the coil measured, and of 

 q\, <74 and Q-i. It is greatest for coils of high Q. 



It is possible to make 3i = — 77 for a given frequency, in which 



case the error reduces to approximately Qq\ and the two errors are 

 of the same order of magnitude for Q = 1, — the error in Re becoming 

 greater, and in L less as Q is increased. 



However, in the general case we cannot cancel qi against ^ over any 



appreciable range of frequencies, and they are normally additive. 

 Also for ordinary inductance coils Q is considerably greater than one, 

 sometimes as large as 100. For such cases the error in Rg becomes 

 large and difficult to determine without an accurate knowledge of the 

 reactances of the resistances used and the losses in the condenser. 



From the above relations we see that a method of this type is 

 capable of measuring inductance with a high degree of accuracy and 

 may be made to measxue effectixe resistance with fair accuracy. 



