2 ALTERNATING CURRENTS 



of changes is spoken of as the period of the alternating current ; and 

 the number of cycles per second is the frequency (sometimes also 

 termed periodicity) of the current. 



In the practical applications of alternating currents, we have to 

 deal with currents whose graphs differ widely from one another. 

 The shape of the graph is spoken of as the wave-shape or wave-form 

 of the current, and is in many problems a matter of considerable 

 importance. In a later chapter, we shall explain how a record of 

 the wave-form or graph of an alternating current may be obtained 

 experimentally. 



Since an alternating current varies from instant to instant, it is 

 obvious that in deciding on a system of measurement, we must define 

 exactly what we mean by the numerical value of an alternating 

 current. 



Now in connection with the most important applications of 

 alternating currents electric lighting, electric power transmission 

 and distribution, electric furnaces the useful effect produced by the 

 current at any instant depends on the value of the square of the 

 current at that instant. Hence, in order that an alternating current 

 may be equivalent (as regards its effect) to a given continuous current, 

 the mean value of the square of the alternating current over a period * 

 must be equal to the square of the continuous current. Otherwise, 

 the two currents are equivalent if the square root of the mean square 

 value of the alternating current is equal to the continuous current. 

 This root-mean-square value is generally termed the r.m.s. value of 

 the current, and when we speak of the numerical value of an alter- 

 nating current, we mean its r.m.s. value. 



In some few cases, we have to consider the arithmetic mean value 

 of a current ; in others, we have to take into account its maximum 

 value. 



The relations connecting the r.m.s., the arithmetic mean, and the 

 maximum values of an alternating current depend on its wave-form. 

 It is usual to consider the ratios of the r.m.s. value to the other two, 

 and in this connection two terms introduced by Dr. Fleming, and 

 known as the form factor and amplitude factor, are convenient. 



mi ^ _r f r.m.s. value 



The form factor of a given wave = 



The amplitude factor 



mean value 



r.m.s. value 

 maximum value 



Hitherto, we have spoken of alternating currents; but all that 

 has been said applies equally to alternating p.d.'s or e.m.f.'s. 



* Or half-period, since the numerical values during a negative half-wave are 

 identical with those during a positive half-wave. 



