INDUCTANCE AND CAPACITY 



359 



should be a perfect condenser in connection with such a resistance 

 that the energy dissipated in the combination is the same as that 

 in the actual condenser. The energy loss may be duplicated by 

 assuming the resistance to be either in parallel or in series with 

 the perfect condenser, as is indicated below. 



Given V, I, P, o>, and assuming sinusoidal currents, 



Series Arrangement 



P = Pr s 

 P 



* rs = 



Parallel Arrangement 



r P 

 V* 



Z P = 



tan = ^-gr- leading tan = cor P C P leading 



Power factor = P.F. = cos 6 

 Phase angle, < = tan" 1 wr s C s Phase angle, = tan" 1 ~ 



To illustrate the foregoing the following measurements of a 

 5-mile length of impregnated paper cable used in power trans- 

 mission may be taken. 



Applied P.D ................. ............ 30,000 volts. 



Current .................................. 10 amp. 



Power supplied to cable .................... 12,000 watts. 



Cycles per second ......................... 60 



From these data: 



12 000 



Power factor = 



= ' 04 



Power-factor angle = 8771, denoted by 6. 



Phase angle = 90 - 8771 = 229, denoted by </>. 



