304 ELECTRICAL MEASUREMENTS 



To illustrate, let the curves of voltage, current, and vi be as 

 shown in Fig. 175. 



f*T 



The net area under the power curve is proportional toJ Q vidt. 



Tj the time of a complete cycle, is proportional to the length of 



1 C r 

 the base line; ~ I vidt is therefore, to the proper scale, the 



1 Jo 

 average ordinate of the power curve. 



In general, when dealing with alternating-current circuits it 



i r 



is necessary to have methods of evaluating ~r 1 vidt. The ex- 



1 Jo 



pression for the power must be left in this general form, for in 

 practical measurements it is not permissible to make any as- 

 sumptions as to the forms of the voltage and current waves. 



For general purposes the simplest and most satisfactory method 

 of measuring the power in an alternating-current circuit is by the 

 use of the electrodynamometer wattmeter. Other methods will 

 be discussed, but their usefulness is restricted to particular cases. 



The Electrodynamometer Wattmeter. It has previously been 

 shown that any electrodynamometer measures the mean product 

 of the currents flowing in the fixed and movable coils; it evaluates 



i r 



f] 



If a Siemens dynamometer is connected to a circuit in the 

 manner shown in Fig. 176, the fixed coils being put in series with 

 the load, while the movable coil, in series with a suitable non- 

 reactive resistance, is placed across the line, the current in the 

 fixed coil, ip, is the instantaneous load current and the current 

 in the movable coil, i M , is proportional to the instantaneous 

 voltage. 



If R is the total resistance of the movable coil circuit, i M = j 



K 



In the case of the Siemens dynamometer with a uniformly 

 graduated scale, 



KD = 



f 



Jo 



K is a constant depending on the windings and on the strength 

 of the controlling spring, and D is the angle through which it is 



