BRIDGE METHODS OF MEASURING IMPEDANCES 467 



Rad = 0. Then the unknown Zx is inserted and the bridge re- 

 balanced. The inductance of the unknown is given, as for Fig. Za, 

 as KRad, but since Cad is unchanged the total resistance in CD is 

 unchanged. Therefore, the series resistance of the unknown will be 

 equal to the change in Rs between the tw^o balances. 



This bridge circuit may be recognized as the familiar bridge due to 

 Owen,^ and it is, theoretically at least, when used as described, an 

 exceedingly desirable bridge for inductance measurements. 



It should be pointed out here that since either Cad or Rs may 

 equally well be used to balance Rx, it is not necessary to use either 

 one or the other exclusively in any one bridge. The adjustments may 

 be combined so that the capacitance adjustment wdll take care of 

 large changes and Rs oi small changes; that is. Cad may be used for 

 coarse adjustment and Rs for fine adjustment. This compromise is, 

 in general, more satisfactory than either method used alone. 



The imaginary product arm type, particularly the form of Fig. 2k, 

 is also well adapted to modification to enable it to measure capacitance 

 and conductance in terms of two adjustable resistances. 



There is a further modification of the substitution method, which 

 is in common use. As already explained, there is little practical 

 advantage in the substitution method for measuring either inductance 

 or capacitance. However, there are occasions w^here the substitution 

 of capacitance for inductance has advantages. Since the reactance of 

 one is opposite in sign to that of the other, the method might more 

 correctly be termed a compensation method, but in common with 

 other substitution methods it can be made irrespective of the type of 

 bridge. Various modifications of the general method may be used, 

 but they are all classed under the general head of resonance methods. 



Resonance Methods 



If it is desired to measure the inductance of any inductive im- 

 pedance, a capacitance standard may be inserted in series with it, 

 and adjusted until the total reactance of the combination is zero. 

 The only function the bridge performs is to measure the effective 

 resistance of the combination and to determine the condition of zero 

 reactance. Any of the bridges of Fig. 2 will do this satisfactorily, 

 but those of real ratio type, that is the simple comparison type, are 

 the most satisfactory since they give the resistance directly in terms 

 of an adjustable resistance standard. This type of bridge is usually 

 termed a series resonance bridge. The value of the inductance is 

 computed from the resonance formula oj^LC =1. It has the dis- 



3 D. Owen, Proc. Phys. Soc, London, October, 1914. 



