44 



ALTERNATING CURRENTS 



E is the vector sum of IR and E z '. The impedance voltage 

 Ez consists of two components, IR' in phase with the current 

 and IX' in quadrature with the current. Therefore, the projec- 

 tion of Ez, the voltage across the impedance, on the current / 

 is the voltage drop due to the resistance of the impedance. 

 Divide this projected voltage by the current and the resistance of 

 the impedance coil is obtained. 



4-i 



(a) (I) 



FIG. 41. Circuit having resistance and impedance in series, and vector diagram. 



Figure 42 (a) shows a series circuit, containing a non-inductive 

 resistance R and an impedance coil Z' in series across the voltage 

 E. Let it be required to construct the vector diagram of this 

 circuit. A voltmeter across the resistance R measures the voltage 

 E R ; when across the impedance it measures the voltage E e > 

 and when across the line it measures the voltage E. 



To construct the vector diagram of this circuit, the current 

 vector 7 is laid off horizontally, as shown in Fig. 42 (6). The 

 voltage E R is laid off to scale in phase with the current /; from 

 the outer end of E R an arc is swung having E z > for its radius. 

 Then from 0, the origin, another arc is swung having E for its 

 radius. Lines drawn from the end of E R and from to the 

 intersection of the arcs complete the vector diagram. By 

 trigonometry the angle 0, the circuit power-factor angle, and <, 

 the impedance coil power-factor angle, can both be found. Know- 

 ing these, it is a simple matter to determine the power-factor and 

 the power of the circuit. 



Example. A resistance and an impedance coil are connected in 

 series across a 60-cycle alternating-current circuit, Fig. 42 (a), and the 

 current is 4.0 amp. The voltage across the resistance is found to be 60 volts, 

 that across the impedance coil 80 volts, and the line voltage is 1 10 volts. Find : 



