158 Dr. Sumpner on the Measurement 



voltage will give the value of sin 6. This method is par- 

 ticularly suited to determine small angles o£ phase-difference, 

 since voltmeters having different ranges may be used, and 

 sin 6 or can be measured as accurately as the two readings 

 can be determined. The method is not always applicable, 

 since the conductors absorbing the voltages to be compared 

 may be in series. In such cases the following bridge 

 method can be used. Suppose that in fig. 2 AB represents 



Fisr. 2. 



r — , / vvvwwvvvvnaA'vvvvvvvvvvvvw 



-AAMAA- 



•tfZKn^r- 



a non-inductive resistance, and B C an inductive resistance 

 in series with it ; the phase-difference cf> between the current 

 flowing through B C, and the voltage across B 0, can be 

 determined by connecting the points A and C to the ter- 

 minals of a suitable non-inductive resistance APC, and 

 finding upon it a point P such that when this point is electri- 

 cally connected with B through a voltmeter the reading v of 

 this instrument is a minimum. The vector figure represent- 

 ing the voltages is shown in fig. 3. In this figure B P 



Fig. 3. 



represents v and is perpendicular to A C. If i\ and v 2 are 

 the voltages A B and B C respectively, the phase-angles 6 

 and -yjr by which these voltages differ from the voltage AC are 

 such that 



sin 6 = 



sin i/r : 



v T 



We also have i\v 2 sin </> = w s where v 3 is the voltage A C. 



