96 CURRENT VALUE. 



.at ' ' 



For inductive circuits 



w = -W =-- -CE cos. 



.'. w = c e cos. <f>. 



The same results may be obtained from slightly different 

 considerations, as follows : 



In Fig. 26, page 59, is shown the curve obtained by mul- 

 tiplying the simultaneous instantaneous values of current 

 and voltage together. This curve, being the product of the 

 values plotted in the sine curves, is itself a sine curve, although 

 displaced above the zero line. Its average value, with due 

 regard to signs, can be shown mathematically to be half its 

 maximum value. For the instantaneous value of the 

 voltage = E sin 0, and the instantaneous value of this 

 current = C sin 0, consequently the instantaneous value 

 of the watts = E C sin 2 0. 



The average value of sin 2 is-^-. 



Hence average watts = -~- C E. 



This has been shown experimentally from the curve on 

 page 59. Its maximum value = C. E = \/ 2c x ^ 2e = 

 2 c e. Consequently the average value of the power curve = 



- = c e. That is, the average power in an alter- 



j-i ' 



nating circuit is the product of .the virtual values of the 

 current and voltage. 



The same statement holds good when the current and 

 voltage are not in phase, if we substitute the energy voltage 

 for the total voltage. The energy voltage is e cos <f> (see page 

 64), and the power in an alternating circuit having an 

 angle of lag is c c. cos <t>. This is, consequently, the value 

 given by a wattmeter, connected to the circuit. The maxi- 



mum value = C E cos </>, and the average value = -- C E 



z 



COS 0. 



It is important to remember that it is the average and not 

 the R.M.S. value of the watts which gives the true power 

 in a circuit. A wattmeter deflection is always proportional 

 to the watts at any instant (and not to watts 2 ), and conse- 

 quently gives the average power. 



