Jfethod of Measuring Energy dissipated in Condensers. 31 

 negative loop from C to D, is given by the integral 



I ^'^=E 1 I 1 cos^>l sin 2 p£ ^ + E^ sin </>| sinptcosptdt, 



EJi jFpt sin2»rr EJj . ,r _ 1» 



1 EJj , 



and this is the work done in — of a second. 



Hence for one second the work done, and therefore the 

 power, is the well-known expression 



P^Ii cos </> = EI cos (E = Ei t/I), 



E and I being the effective values of the electromotive force 

 and current. 



The area of the positive loop, which represents the work 

 done upon the condenser in charging it, is 



and the area of the negative loop, which represents the work 

 done by the condenser in its discharge, is the value of the 

 same integral between the limits tt— <£, and ir, for pt. 



The efficiency is the ratio of the work done by the condenser in 

 its discharge to the work done upon the condenser in charging 

 it. 



This is the gross efficiency, r\. 



mi- . oqo Area of the Negative loop _ l/^E 1 I 1 x "48638 _ Q , „- 



Taking <£ = 89°, V = Area f Positive loop " l/pE&x '51378 ~ 94 6 ? % 



i. *=87°,? = „ = S= 84 * 75 % 



„ (£ = 45°, *? = = = 6-38 o/ 



Having found the angle <£ by the wattmeter measurements 

 the gross efficiency of the condenser may be found from the 

 above equations, or taken from fig. 9, which is drawn from 

 them. 



