296 



PRINCIPLES OF ELECTRICAL DESIGN 



imagining the actual wave to be replaced by a so-called equiva- 

 lent smooth wave; but the use of equivalent sine- waves for 

 power calculations on practical A.C. circuits, can generally be 

 justified. An equivalent sine- wave may be denned as a sine- 

 wave of the same periodicity and the same virtual value as the 

 irregular wave which it is supposed to replace. An equivalent 

 sine-wave of current would produce the same heating effects as 

 the irregular wave; but its mean value, and therefore its form 

 factor, may be different. 



A sine-wave plotted to polar coordinates will be a circle, of 

 which the diameter representing the maximum value of the 

 sine- wave is easily calculated since the equivalent wave must 



FIG. 121. Irregular wave and equivalent sine wave plotted to polar 



coordinates. 



have the same root-mean-square value as the non-sinusoidal 

 wave, and therefore also the same area when plotted to polar 

 coordinates. 



Let d = the diameter of the equivalent circle (or maximum 



value of the equivalent sine-wave) 

 and let A = the area of one lobe of the irregular wave plotted to 



polar coordinates, 

 then 



whence 



(108) 



