438 ELECTRICAL MEASUREMENTS 



tivity is to be maintained, and is defined as the fractional change 

 in the frequency of the current which will reduce the sensitivity 

 of the instrument to one-half its maximum value. It is highly 

 desirable if the galvanometer is to be used for general laboratory 

 purposes, that the resonance point be not too sharply defined. 

 That is, the resonance range of the instrument should be large, 

 as great as 0.2 of 1 per cent. 



To express the resonance range in terms of the constants of 

 the galvanometer: 

 when the instrument is perfectly tuned, 



< . ,,_. 



If the frequency of the supply is slightly raised, that is, if N is 

 made a little greater than 1, the deflection becomes 



_ <X* 

 a>\/P 2 w 2 [l - N 2 ] 2 + k 2 N 2 



In determining the resonance range the change in N is supposed 



to be such that 7^ = ^4- so 

 1 N 21i 



= P 2 o> 2 [l - N 2 ] 2 



and as N is very nearly 1, 



k\/3 



I N 2 = j; i approximately. 

 ru 



_ Frequency of current which halves the maximum amplitude _ 

 Resonating frequency 



where R* is the resonance range for current. 



k\/3 



'- ^ = on > approximately. (59) 



2 r& 



Voltage Sensitivity. 31 When a vibration galvanometer is so 

 used that the voltage sensitivity is important, it should be noted 

 that as the coil vibrates it cuts the flux in the air gap and thus 

 sets up a back e.m.f. which is in time quadrature with the de- 

 flection and has a component in opposition to and a component 

 in quadrature with the current. 



The e.m.f. which is effective in forcing the current through the 



