440 ELECTRICAL MEASUREMENTS 



The corresponding maximum value of 0, obtained by 63 and 61, is 



V 



In general the equivalent impedance of the circuit including 

 the galvanometer is 



r CVfc -1 . r C'PItt.' - a*) -] 



f PW-] * + L + ' (( 



when conditions (63) are imposed, this reduces to 



Z = 2r + jo. 



Therefore, when the deflection has been made a maximum by 

 adjusting both T and C the current is in phase with the applied 

 voltage and 



7 = 



In this case half the energy supplied to the instrument is ex- 

 pended mechanically and half in electrical heating. 



The sensitivity to a voltage whose frequency is N times the 

 resonating frequency may be seen from (61). If the voltage, 

 V N) is applied at the galvanometer terminals, 



ff = 



a PP roximatel y- 



By a process similar to that used on page 438 it may be shown 

 that the resonance range for voltage, R v , is 



C 2 ) approximately (67) 



V 



2.TTCO 



It may be possible to increase the voltage sensitivity of the 

 galvanometer by applying the potential difference through a 

 step-up transformer of the proper ratio. The step-up ratio, 

 A, required for maximum sensitivity is given by 



where r { is the resistance of the primary and r that of the galva- 



nometer circuit. By the use of a transformer of the above ratio 



^ 



the voltage sensitivity is increased in the ratio " 



