Formulae used in Inductance Measurements. 



795 



Hence 



c l R 1 = 6 , 2 R 2 

 ( , 1 L 1 a) = t' 2 L 2 ct) 



R, = L, 



R 2 L 2 



Hence both these conditions must be fulfilled in order that 

 a balance may be obtained. The method is evidently much 

 more easily employed if one of the inductances is variable. 

 It is further considered later. 



Comparison of Two Mutual Inductances [Maxwell's Method]. 



Fiff. 2. 



Circuit Diagram 



cR 2 P S 



Vector Diagram 



Here the points 0! and 2 are at the same potential, so the 

 fall in potential due to the impedance of the arm 0]A0 2 

 must be balanced by the E.M.F. due to the current c' in the 

 primary of the mutual inductance M x . The triangle OPQ 

 represents the vector diagram of this arm. The same cur- 

 rent c flows in the arms OxA0 2 and 2 B0 1? and the current c 

 in the primaries of the two mutual inductances is also iden- 

 tical. Hence the triangle OST representing the vector 

 diagram of the arm 2 B0i is similar to OPQ. 

 Hence 



cR : _ cLiO) _ ^MjG) 



cR 2 ch 2 co c'M 2 o>' 



so 



Ri 



R 2 



h 



L 2 



M 2 * 



Hence a perfect balance can only be obtained if the self- 

 inductances are in the same ratio as the mutual inductances. 

 If, however, we make the non-inductive resistances in series 

 with the coils L t and L 2 large, the angle <f> will become very 



smaJ 



.ml 



a fair balance wil 



be attained when-, - 1 = 



R 2 ~ M s 



3F2 



