INDUCTANCE AND CAPACITY 439 



circuit is the vector difference of the applied and the back 

 e.m.fs. 



The back e.m.f . is given by 



coC 2 / 



J P[co 2 - co 2 ] + jku 

 -/co 2 C 2 /c-j/coC 2 P[coo 2 -co 2 ] 

 P 2 [co 2 - co 2 ] 2 + fc 2 co 2 



If r and L are the resistance and inductance of the reactive circuit 

 in which the galvanometer is inserted and V is the applied voltage, 



I(r + jcoL) = V + E B 

 and '- 



CV 



rP[co 2 - co 2 ] - fcco 2 L + jco[/cr + LP(co 2 - co 2 ) + C 2 ] 



In this case, where the circuit is reactive, the sensitivity is not 

 a maximum when co = co but when T is so adjusted that 



']-- - (62) 



The corresponding value for the magnitude of 6 is 



r62 . 



= 



From (62) and (62o) it is seen that if C is large it may be possible 

 to increase the deflection by placing an inductance in series with 

 the galvanometer and slightly raising the frequency of the 

 supply, for the fractional increase in the numerator of (62a) may 

 be greater than that in the denominator. 



To obtain the greatest possible deflection when the instrument 

 is used in a circuit of fixed inductance, both the torsional con- 

 stant of the suspension, T, and the coil constant, C, must be 

 adjusted. C may be varied by changing the strength of the flux 

 threading the coil. When both T and C are adjusted, the 



magnitude of 6 is a maximum when 



C 2 co 2 L 



P((00 2 - CO 2 ) == - 2 22 



and 



(63) 



