36 



ALTERNATING CURRENTS 



19. Circuit Containing Resistance, Inductance and Capaci- 

 tance in Series. Figure 35 shows a resistance R, an inductive 



reactance X L and a condensive reactance X c , all connected in 



series. The voltage across the circuit is E volts, the frequency 



is / cycles per second and the current 

 is / amp. 



As this is a series circuit, the current 

 is the same in all parts of the circuit 

 and for convenience the current vector 

 / is laid off horizontal in the circuit 

 vector diagram, Fig. 36. The voltage 

 E R ( = IR) across the resistance is in 

 c phase with the current and is laid off 

 to scale along the current vector. 

 The voltage E L (= IX L ) across the 

 inductance is laid off at right angles 

 to the current and leading. The 



voltage EC (= IX c ) across the condenser is laid off at right 



angles to the current and lagging. 



An examination of Fig. 36 shows that the voltage across the 



inductance and that across the capacitance are in opposition, 



so that the resultant voltage of 



these two is their arithmetical 



difference. In this particular 



case, IX L is shown as being 



greater than IX C . Therefore, 



IX c is subtracted directly from 



IX L . The line voltage must be 



the vector sum of the three 



voltages and is the hypotenuse 



of a right triangle of which IR and (IX L IX c ) are the other 



sides. Therefore 



FIG. 35. Circuit containing 

 resistance, inductance and ca- 

 pacitance in series. 



IR 



.IX, 



I- 



IX, 



FIG. 36. Vector diagram for cir- 

 cuit containing resistance, inductance 

 and capacitance, all in series. 



E = 

 E = 



(IX L - 



Solving for 7 



+ (X L - X c ) 2 



E 



(20) 



(21) 



