THEORY OF TRANSFORMER. 97 



Whence the current and applied P.D. are in phase that is, there 

 is electrical resonance in the primary circuit, if 



= .... (16) 



that is, for a given primary reactance there are two values of the 

 secondary reactance for which resonance may occur in the primary 

 circuit, provided the roots of equation (16) considered as a 

 quadratic in s 2 are real ; that is, if 



is greater than 



If p 2 M 2 = 2sir 2 these two values coincide, and s 2 = r 2 , i.e. the 

 secondary resistance and reactance are numerically equal. 



Equations (14) show that the apparent resistance of the 

 primary circuit is increased, and its apparent reactance is 

 diminished by the presence of the secondary circuit. 



From equation (12) we see that the secondary current lags 

 behind the primary P.D. by an angle TT ^, where 



It is evident from this that the secondary current is in exact 

 opposition to the primary applied P.D., if 



*Va - sis 2 + p*M* = ..... (18) 



and this condition is satisfied by one value only of s 2 . Moreover, 

 conditions (16) and (18) cannot be satisfied simultaneously, since 

 then we should have 



r&i = 



and the secondary current would be infinite, as is seen by reference 

 to equation (12). 



If condition (16) is satisfied, we see from equation (11) that 

 the primary current is given by 



n + -V 2 



which shows that, even if the primary current is in phase with the 

 impressed P.D., its value depends upon the resistance of the 

 secondary circuit, and the ratio of the reactances of the two 

 circuits, as well as upon the primary resistance. 



II 



