CURRENT VALUE. 89 



A little care will have to be used in deciding which points 

 near the zero line are positive and which are negative, since 

 the voltmeter will always give readings in the same direction. 

 If the contact maker is moved rapidly at this point, the sign 

 of the voltage may change before the voltmeter needle has 

 time to go to zero and rise again as the zero point is passed. 

 By moving the contact maker slowly, and carefully watching 

 the voltmeter, the approximate point of reversal can be 

 obtained with certainty ; the exact point can only be seen 

 after plotting the curve. As already mentioned, the use of a 

 battery is a great assistance at this part of the curve.* 



Comparison of Values of Alternating and Direct Current. 

 The simplest standard of comparison between an alternating 

 and direct current is that of their heating effects when passed 

 through a resistance, since this is independent of direction 

 and dependent only on the strength of the current. 



The rate at which heat is developed in a conductor whose 

 resistance is R ohms is C 2 R joules per second where C = 

 current in amperes. Thus a direct current of C amperes 

 would develop C 2 R joules in one second. An alternating 

 current of equivalent value will also develop G^R joules in 

 one second. Hence the alternating current of C amperes, which 

 is equivalent to a direct current of G amperes, must be such 

 that the average value of (7 2 (alternating) = average value 

 of C~ (direct), i.e., ^ average value of C 2 alternating = 

 \/ average value of C' 1 direct. 



Now /y/the average value of G 2 direct is C direct, but 

 \/ the average value of (7 2 alternating is not the same as the 

 average value of G alternating. 



The fact that the *J average value of n 1 is not equal to 

 the average value of n can be shown at once by taking a 

 numerical example. 



For instance, the average value of the numbers 1,2, 3, 4 is 

 1+2 + 3 + 4 10 - 



* A slight modification of the arrangement shown in Fig. 41 enables the 

 low values of cvirrent and voltage to be measured with increased accuracy. 

 By connecting the voltmeter to read alternately the voltage across r, R and 

 R -\-r (instead of R and r -f- R only), the separate readings will check each 

 other. Thus, since the quantities read are instantaneous values, the sum of 

 the voltages across r and R must be equal to the voltage of R + r, and thus 

 the two readings across the separate resistances should always be together 

 equal to the third reading. Since the circuit is inductive, it will seldom 

 happen that more than one of the quantities is small at the same time. Thus 

 the value of a low reading can generally be calculated as the difference of two 

 readings of more convenient magnitude. 



