THE TRANSFORMER. 167 



which the current to be measured passes successively, when 

 the dynamometer is used in the usual manner. It is, however, 

 usually possible to disconnect these coils, and different 

 currents can then be sent through each. In any case the 

 reading of the instrument Hs proportional to the mean 

 product of the currents in each coil. Thus, when reading a 

 single current, the deflection = k c? where k is a constant, 

 and c 2 is the average value of the square of the current. 

 If the same instrument has two different currents, e t and C 2 , 

 flowing through the two coils, its deflection will be k c l c 2 , 

 where Cj e 2 is the average value of the product of the two 

 currents. If these two currents are not in phase with each 

 other, but differ by an angle a > we may consider one current 

 c., as equivalent to two components 90 apart in phase, 

 one component C 2 cos a being in phase with Cj and capable 

 of producing a deflection of the dynamometer. The other 

 component will be c 2 sin a, exactly a quarter period out of 

 phase with <\ and incapable, therefore, of producing any 

 resultant action on the dynamometer. 



In such a case the deflection of the instrument will be 

 entirely due to c l and the component of c 2 , which is in 

 phase with c^ Hence deflection = k (mean value of c l c 2 

 cos a ). The principle of the behaviour of the dynamometer 

 is in this case exactly similar to that of the wattmeter already 

 discussed on page 57. 



Suppose a dynamometer to have one coil inserted in the 

 primary circuit of a transformer, and the other coil in the 

 secondary circuit, the latter being non-inductive. Then, 

 if Cj c 2 are the instantaneous values of primary and 

 secondary current, and a is the angle of phase difference 

 between the two currents, the reading of the dynamometer 

 will be the average value of c l c 2 cos a, which may be written 

 for convenience c t c 2 cos a. 



As will be explained more fully later in connection with 

 transformer diagrams, in a transformer with a non-inductive 

 secondary load, the phase angle between the primary and 

 secondary currents is (180 angle of lag of primary circuit) 

 = 180 , where is the angle of lag of primary 

 circuit. Hence the reading of the dynamometer when con- 

 nected so as to have the primary current in one coil and 

 secondary current in the other, will be 



k. c t c 2 cos (180 <p) = - k c l r 2 cos 0. 



