ALTERNATING-CURRENT CIRCUITS 



which is the equation for the scries alteniat in^-eurrent circuit 

 in the steady state. 



The value of X L and X c may be substituted in equation 



(21). It then becomes 



7 = ! (22) 



'11 ie phase angle 6 is found as follows: 



tan 6 = XL ^ Xc (23) 



If X L is greater than A',, the tangent is positive and 6 is 

 positive, as shown in Fig. 36. This indicates a lagging current. 

 is greater than X L , the tangent becomes negative and the 

 angle 8 becomes negative. This indicates a leading current. 



The power-factor of the circuit 



P. F. = cos e = - -^- = h> (24) 



(X L - 



Example. A series circuit consisting of a resistance of 50 ohms, acapaci- 

 t;ui( < of 25 mf. and an inductance of 0.15 henry is connected across 120- 

 O-cycle in 



I-'iml: n The impedance of the circuit. (6) The current in the circuit. 



Itage across the resistance, (d) The voltage across the induc- 



tance ( i The voltage across the capacitance. (/) The power taken by the 



circuit, (g) The phase angle of the circuit. (//) The power-factor of the 



circuit. 



- 2r60 X 0.15 = 377 X 0.15 = 56.6 ohms. 



Xc " 2^0 X 0.000025 



= \/(50) + (56.6-106) 1 = v / (50) t + -70.2ohm 



1 J< ) 

 (b) / 





//,' = 1.71 X 50 - 85.5 volts. Ans. 

 - /XL- 1.71 X 56.6 - 96.8 volts. Ans. 



= 1.71 X 106 = 1X1.1 volts ,\na. 

 /> - /f/2 , (1.71) 1 X 50 - 146 war 



56.6 - 106 - I 1 .'. I 

 in ' = r,o ao 



$ - -44.6. Then-fop- tb leads. Ana. 



" s '- ^r- 



