126 ELECTRICAL MEASUREMENTS 



The air damping is very small so n = C0i, approximately. This 

 relation may be proved directly as follows. 



Let n = number of linkages of flux with exploring coil. 

 0! = final value of deflection. 

 C = coil constant. 

 o> = angular velocity of movable coil. 



= rate ^ c ^ ange ^ Images through exploring coil. 



\di) 



L = inductance of exploring coil circuit. 

 P = moment of inertia of movable system. 

 k' = damping constant for air damping. 



r = resistance of exploring coil circuit. 



i = current at any instant. 

 N' = number of turns in exploring coil. 

 <p = flux through exploring coil. 



As soon as the coil begins to move, it sets up a back e.m.f. whose 

 value is coC. 

 The current at any instant is 



dn di 



and 



_ _ C (dn\ C 2 o> CL di 

 dt = 



C (dn\ C 2 o> CL di 



i - co = - (-J-) -j- - k'w. 



r \dl/ r r dt 



At the beginning and at the end of the deflection, both w and 

 i are zero, so on integrating, 



The air damping is small. Very closely then the change of flux 

 linkages is given by 



n = C0i 

 and 



C0! 



