ROOT MEAN SQUARE VALUES OF ALTERNATING CURRENTS. 33 



Balances ; amongst those for the measurements of E.M.F.s 

 are Electrostatic and Hot Wire Voltmeters. 



It is of importance, therefore, to clearly understand what it is 

 that is actually measured by alternating-current instruments. 



It has been stated that the deflections are proportional to the 

 mean square of the quantity to be measured. 



The instruments may be provided with a uniform scale and 

 the square root of the reading taken as a measure of the current or 

 E.M.F., or they may be graduated to read direct, in which" case 

 the scale will not be uniform. Whatever way the instrument is 

 graduated, the quantity measured is, therefore, a root mean 

 square value. 



ROOT MEAN SQUARE VALUES. 



27. The reason why root mean square values are taken in 

 alternating- current measurements is obvious, for since the average 

 value of a periodic current is zero, an instrument in which the 

 deflection is proportional to the current would show no deflection, 

 and it is necessary to employ instruments which are deflected in 

 the same direction whatever be the direction of the current through 

 them, that is, we must employ instruments which measure the 

 mean square of the periodic quantity 



i = I sin pt 



where i is the instantaneous value of the current at any time t ; 

 p = 2-irn, n being the frequency ; and I is the maximum value of 

 the current. 



The root mean square value of the current is obtained by 

 dividing half the periodic time into an infinite number of parts, 

 taking the sum of the squared values of the current at each of 

 these points, dividing this sum by half the periodic time, and 

 extracting the square root of the result. 



The periodic time is , so that half the periodic time is 



P P 



If we write A for the root mean square current, we have, 

 therefore 



(15) 



