ALTERNATING CURRENT MEASUREMENTS. 49 



cates watts correctly on a direct- current circuit, it will indicate 

 watts correctly on an alternating-current circuit. 



Inductance error of the wattmeter. This discussion applies only to harmonic 

 electromotive force and current, and it presupposes a knowledge of Chapters III and 

 IV. Let the line OE in the clock diagram, Fig. 39, represent the electromotive 



Fig. 39. 



force between the supply mains, the line Ofj, the current delivered to the receiving 

 circuit, and the line OI a the current (generally very small) in the circuit AR, Fig. 

 38. The diagram shows the current I a in phase with E which would be the case 

 if the circuit AR, Fig. 38 , were absolutely non-inductive. The effect of a small 

 amount of inductance in the circuit AR is to turn I a "very slightly towards I^ t thus 

 lessening the angle between I a and /& by the small amount A0, but without pro- 

 ducing an appreciable decrease in the value of I a . 



The average value of the product of the currents in the two wattmeter coils is 

 / a /6 cos 6, the force action between the coils is proportional to this average product, 

 and the deflection D is proportional to the average force action. Therefore we may 

 write 



D = klah cos 



in which k is a constant. The change of reading AZ> due to the decrease, A0, in 

 the angle 6 is 



AZ> = kl a h sin 6 A0 



Therefore, the actual wattmeter error, AZ?, due to inductance in the circuit AR 

 is zero when the receiving circuit is non-inductive (sin 6 = 0], and it increases with 6 

 and reaches a maximum when the receiving circuit is very highly inductive (sin 6-= I ) ; 

 and the percentage error of the instrument, namely, &DJ D (=tan 6 A0) is equal 

 to zero when the receiving circuit is non-inductive, and it becomes indefinitely large 

 when the receiving circuit is highly inductive, that is when 6 approaches 90. 



20. The watt-hour meter is an instrument for summing up the 



total work or energy delivered to a circuit. There are two types 



of watt-hour meter in general use, namely, the commutator-motor 



type and the induction -motor type. The commutator-motor type 



5 



