96 



TREATISE ON ALTERNATING CURRENTS. 



E.M.F., ks&z, due to the secondary reactance. We thus have the 

 vector E.M.F. equation 



/ 2 i-2 -f ks. 2 i-2 = I'pMii 



or 



r*k + a*a + kpMk = ...... (10) 



Equations (9) and (10) are the vector E.M.F. equations of the 

 primary and secondary circuits respectively. Eliminating first ij 

 and then i\ we get 



(Ova - *ia 4- y/ 2 J/ 2 ) -f /.'(/'I 4-*, r&i)}ii = (v, 

 and 



which may be written in the forms 



and 



-f * a 2 ) - 



. (11) 



i 3 -f /J/ 2 )H 2 = pJ/^ . . . (12) 



Hence the magnitudes of the primary and secondary 

 currents are given by 







vF + *+^5^^ 



pMe 



/ (13) 



If 7? and ^ are the equivalent resistance and reactance of the 

 primary circuit, we get at once from equation (11) 



u - 



and 



(14) 



From equation (11) we also see that the primary current lags 

 behind the applied P.D. by an angle where 



. I 1 ) 



_ 



Idll U - '- n . n^. - - o -- Ta 



ri(r -f tf) 



