108 



TREATISE ON ALTERNATING CURRENTS. 



TABLE VI. 



FREQUENCY 100 CYCLES PER SECOND. 

 Transformation Ratio. 



PROBLEMS ON CHAPTER XI. 



1. Show that, if the primary and secondary coils of a transformer arc so 

 wound that there is no leakage, the equivalent self-induction of the primary 

 circuit with closed secondary is given by 



where L l and L 2 are the self-inductions of the primary and secondary coils 

 respective!)', r 2 is the total resistance of the secondary circuit, and p = 2irn, n 

 being the frequency, the secondary external circuit being non-inductive. 



2. Assuming the result given in Question 1, show that in a transformer 

 having no leakage, and non-inductive external secondary circuit, the primary 

 current lags behind the applied by P.D. an angle </> given by 



tan <> = 



-f- p*L 2 ( ri L 2 + 



where r, is the resistance of the primary coil. 



3. Show that, in a transformer having no magnetic leakage, the impedance 

 of the primary on closed non-inductive secondary circuit is greater than, equal 

 to, or less than its impedance on open secondary, according as A/2r { r 2 is greater 

 than, equal to, or less than pM, where r x is the resistance of the primary coil, r 2 

 the total resistance of the secondary circuit, M the mutual induction of the 

 primary and secondary coils, and p = 2vn, n being the frequency. 



