supplied to the Primary Coil of a Transformer. 485 



This method of calculating the mean power supplied to the 

 primary of a transformer is, however, inconvenient, as it 

 entails the use of a high-resistance dynamometer, with which 

 two observations must be taken to obtain L x , in addition to 

 the trouble of adjusting the resistances of the two circuits to 

 obtain the same conditions as when the wattmeter-reading 

 was taken. 



The following method, in which a high-resistance electro- 

 dynamometer is employed, enables the power given to the 

 primary coil to be measured from one reading without the 

 knowledge of either the resistance or the coefficient of self- 

 induction of the primary. 



Let the two coils of the electrodynamometer be A and B, 

 and let their resistances and coefficients of self-induction be 



i\ r 2 and l x l 2 respectively ; moreover, let — = — , that is to say, 



let the time-constants of the two coils be the same ; this can 

 be easily effected by putting an inductionless resistance in 

 series with one or other of the coils. Connect as in the 

 diagram. 



/VvVYvvvv. 



vt nnry?r?nnr^^vwwvvv i 



Let the primary coil be put in series w T ith an inductionless 

 resistance R. Let the potential-difference between Vj and V 2 

 = E 1 sina£ ; then i, the current through the primary coil and 



through E= -^ sin (at—ty), where E 2 is the maximum poten- 

 tial-difference between V 2 and V 3 . 



Let -^i and \jr 2 be the angles of lag of the coils A and B 

 respectively, and let ?', and i 2 be the currents through them at 

 some instant t. 



Then, if S be the reading of the torsion-head, 



8=nr hh dt, 



= 7£ • ~g-^ I sin (at - fa) sin (at - i/r - yjr 2 ) dt, ' 

 k LjE 2 



■> 



SiS, 



cos^i— \fr 2 — yfr); 



Phil. Mag. S. 5.. Vol. 25. No. 157. June Mit&. 



