380 ELECTRICAL MEASUREMENTS 



From the above, 



v = R[Ii sin co -f / 3 sin (3co2 3 ) + /6 sin (5co 5 )-f . . .] 

 -f coL [/i cos co -f 3/3 cos (3co 3 ) + 5/ 5 sin (5coi 5 ) -f . . . ] 



The mean square value of the P.D. will be 

 therefore, 



CO/ 



When the resistance is negligible, 



In this case, suppose the P.D. wave has been analyzed. Then at 

 any instant, 



v = Vi sin wt + F 3 sin (3co/ - 3 ) + V b sin (5w^ - 5 ) + . . . 

 Therefore 



- Li = cos orf + -5-*- cos (3orf - 3 ) -h -r 1 cos (5o>< - 5 ) + . . 



0) 5CO OCO 



The mean square value of Li will -be 



7 272 I I I 



9 O I r\ O O I O CT O O ~" 



and 



= _JL VV , 1 JV J^ F^ 

 /coF \ 2 ' 9 ' o i oc * o 



2 ' 25 2 



or 



- J- /tV + W 



- / V" Fi* + Fa 



+ F 6 * + 



Capacity Measurements. The current through a condenser 

 with a perfect dielectric is given by 



1 - c * 



