250 ELECTRICAL MEASUREMENTS 



kept constant, a small amount of work will be done which is 

 numerically equal to the change of electrical energy. If M is 

 the moment causing the displacement of the needle, then as 



Similarly M F = (V + d) 2 - 



The net turning moment acting on the needle will be 



M 



This moment is balanced by the torsion of the suspension, so 

 if D is the deflection and T the torsion constant 



r 2 _ r] 2 



rD = j^y [2V d + d 2 ] in absolute electrostatic units. (6) 

 If volts are used, 



The quadrant electrometer is always used as a secondary in- 

 strument, but the formula (7) is useful as an aid in preliminary 

 design. 



The instrument is read by one of the mirror and scale methods, 

 so if D be taken in scale units, 



D = K[2Vd + d 2 ] (8) 



An equivalent expression is frequently used, 



(9) 



Here, Vi, V z and V are the potentials of the two sets of quad- 

 rants and of the needle respectively. 



If the potential differences are alternating, the instantaneous 

 value of the turning moment is proportional to 2Vd + d 2 and 



(2Vd + d 2 )dt. 



PROPERTY CF ELECTRICAL LAB IRATOI 



FACULTY OF APPLIED SCIENCE. 



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