PROBLEMS. 39 1 



Note. See Arts. 10, II, and 12 of Appendix A for a discussion of the 

 condenser. 



CHAPTER V. THE USE OF COMPLEX QUANTITY. 



54. An alternating current of 100 amperes flows in a circuit. Choosing the cur- 

 rent vector as a reference axis, the two components of E are 700 volts and 200 volts 

 respectively ; that is, E = 700 volts -\-j X 2O volts. Find the resistance and the 

 reactance of the circuit. Ans. 7 ohms resistance and 2 ohms reactance. 



55. An alternating electromotive force of 1,000 volts acts on a circuit. Choosing 

 the electromotive force as the reference axis, the components of 7 are 75 amperes 

 and 20 amperes ; that is, /= 75 amperes -\-j X 20 amperes. Find the resistance, 

 reactance, impedance, conductance, susceptance, and admittance of the circuit. Ans. 

 12.45 ohms resistance, 3.32 ohms reactance, 12.88 ohms impedance, 0.075 recip- 

 rocal ohms conductance, 0.02 reciprocal ohms susceptance, 0.0776 reciprocal ohms 

 admittance. 



56. The components of the current specified in problem 54 with reference to an 

 arbitrary axis are 80 amperes and 60 amperes respectively ; that is, 7 80 amperes 

 -\- j X amperes. The resistance of the circuit is 7 ohms and the reactance of the 

 circuit is 2 ohms. Find the components of E with reference to the same arbitrary 

 axis. Ans. ^--component 440 volts, y component 580 volts. 



57. Given E 100 volts -{- j X 6 volts and 7=3 amperes / X 2 amperes. 

 Find (a) effective values of E and 7, (6) power delivered to the circuit, (c) re- 

 sistance of the circuit, (d) reactance of the circuit, (<?) impedance of the circuit, (f) 

 conductance of the circuit, (g) susceptance of the circuit, and (h] admittance of the 

 circuit. Ans. (a) 116.6 volts and 3.61 amperes, (b] 1 80 watts, (c) 13.85 ohms, 

 (d] 29.23 ohms, (e) 32.35 ohms, (/") 0.01324 reciprocal ohms, (g) 0.02794 recipro- 

 cal ohms, and (h} 0.03091 reciprocal ohms. 



Note. It is instructive in calculating power to use the formula on Art. 45, page 

 95, and also to use the formula 7*= ^7*. 



58. An electromotive force of which the components are 50 volts and 75 volts re- 

 spectively ; that is, E 50 volts -\-j X 75 volts, produces a current through a cir- 

 cuit of which the resistance is 10 ohms and the reactance is 6 ohms. Find the 

 components of the current and find the power delivered to the circuit. Ans. ^--com- 

 ponent of current 0.368 amperes, /-component of current 7.72 amperes, power 597.5 

 watts. 



59. Separate the components of the complex expression 



Ans. Real component - 



f(ac-\- bd} -f e(bc a 

 /-component J - ~^f^- 



60- Separate the components of the complex expression 



