Method of Measuring Energy dissipated in Condensers. 29 



as in the second, and this requires a relatively large shunt 

 current. 



A modification of the method, if a second small transformer 

 is available, is to transform down again to a low voltage, and 

 put the shunt circuit of the wattmeter on the low voltage 

 secondary of this second transformer. The current will now 

 be almost exactly opposite in phase to the high electromotive 

 force at the terminals of the condenser, and by interchanging 

 the terminals the wattmeter deflexion will be the same as 

 before, if the shunt resistance is reduced in the ratio of trans- 

 formation. The currents in the two coils of the wattmeter 

 are so nearly in phase with one another that a small change 

 in the phase of the shunt current will produce no appreciable 

 error. 



The Efficiency of a Condenser. 

 Having thus determined the energy, w, dissipated in a 



condenser, by wattmeter measurements, we 

 readily find r s , the equivalent resistance of the 

 condenser, from the expression 



10= IV. 



The ratio of the equivalent resistance to 



c P 



is cot $ (fig. 7) , <f> being the angle of advance 



of the current ahead of the electromotive force. 

 It remains to calculate the efficiency of a con- 

 denser. 



In fig. 8 I is the current flowing into and 

 out of the condenser, assuming both current 

 and electromotive force to be simply harmonic. 

 The dotted curve is the power curve. 



^=E X sin pt j 



where 0=the instantaneous E.M.F. acting on 

 the condenser, and E x is its maximum value. 





E x 



sin (pt-{-cj)) = I 1 sin {pt + <f>), 



Fig. 7. 



Impedance 



£?' =E 1 I 1 sin pt sin (pt + </>) 



= EJi [sin 2 pt cos $ + sin pt cos pt sin <£] . 



The area of the power curve for one half-period, that is the 

 area of the positive loop from B to C, minus the area of the 



