46 



ALTERNATING CURRENTS 



24. Polygon of Voltages; Four Voltages. If three sides of a 

 triangle are fixed, the triangle itself is fixed as regards both its 

 area and its angles. If the four sides of a polygon are given, 

 however, the polygon itself is not determined. In order to 

 determine the polygon definitely, the angle included between two 

 of its sides must be known. This is the condition which exists 

 when there is resistance, inductance and capacitance in a series 

 circuit. These three voltages and the line voltage give four 

 voltages which in themselves make an indeterminate polygon. 

 If the angle between two of these voltages is known, the polygon 

 and its angles are completely determined. 



(a) 



FIG. 43. Polygon of voltages for series circuit containing resistance, inductive 

 impedance and capacitance. 



This is illustrated in Fig. 43, in which resistance, impedance 

 and capacitance are all connected in series and the current / 

 flows in the circuit. Assume that the condenser power-factor angle 

 is 90, which is practically the case in most commercial condensers. 

 This constitutes the angle which determines the polygon of voltages. 

 Along / lay off E R to scale, Fig. 43 (6). Ninety degrees behind / 

 lay off EC to scale. Add these two vectorially giving E' = 1k 

 + # c . From the end of E r swing upward the vector EJ and 

 from swing the line voltage E. Complete the polygon whpre 

 these two arcs intersect. Then from again draw E z ' parallel to 

 the Ez swung from the end of E'. 



It will now be seen that 



