118 ELECTRICAL ENGINEERING 



The power factor of a circuit is the ratio of the true power to 

 the apparent power and is 



P El cos </> 



EI = TT 



therefore, the power factor is the cosine of the angle of phase 

 difference between the current and the impressed e.m.f.; it is 

 usually expressed in per cent and may be either leading or lagging. 



When the current is in phase with the e.m.f., the power factor 

 is unity or 100 per cent. 



When the current leads the e.m.f. by 60 degrees the power 

 factor is 50 per cent leading, since cos 60 = 0.5; when the current 

 lags behind the e.m.f. by 60 degrees the power factor is 50 per 

 cent lagging. 



The sine of the angle of phase difference between the current 

 and the impressed e.m.f. is called the inductance factor of the 

 circuit. 



81. Examples. (1) If an alternating e.m.f. of effective value 

 E is impressed on a non-inductive circuit of resistance R, a cur- 

 rent / will flow in phase with the e.m.f., where 



i-?. 



R 



The vector diagram is shown in Fig. 86. 



(2) If an alternating e.m.f. E is impressed on a circuit of re- 



E 



actance X and negligible resistance, a current / = ^ will flow 



lagging 90 degrees behind the e.m.f. (See Fig. 87.) 



(3) If an alternating e.m.f. E is impressed on a circuit of re- 

 sistance R and reactance X, a current I will flow lagging behind 



the e.m.f. by angle 0, where 



% 



tan < = -^ 



The vector diagram for the circuit is shown in Fig. 88. The 

 e.m.f. consumed in the resistance is EI = IR volts in phase with 

 the current and is represented by the vector OEi. 



The e.m.f. consumed by the reactance is E 2 = IX volts leading 

 the current by 90 degrees represented by OE 2 . The impressed 



e.m.f. is OE = E and is the vector sum of E\ and E^; therefore 



E= VES + ES = vn+TX = IR* + X 2 = 7Z, 



