Chapter 20. -SHIPBOARD ELECTRICAL SYSTEMS 



where 



•71 

 f 



L 



inductive reactance, in ohms 



3.1416 



frequency, in cycles per second 



inductance, in henrys 



The current flowing in a capacitive circuit 

 is directly proportional to the capacitance and to 

 the rate at which the applied voltage is changing. 

 The rate at which the voltage changes is deter- 

 mined by the frequency. The value of the capaci- 

 tive reactance, Xq, is inversely proportional to 

 the capacitance of the circuit and the frequency 

 of the applied voltage. Thus, 



1 



27rfC 



where 



TT 

 f 



c 



= capacitive reactance, in ohms 

 = 3.1416 



= frequency, in cycles per second 

 = capacitance, in farads 



The effects of capacitance and inductance in 

 an a-c circuit are exactly opposite. Inductive 

 reactance causes the current to lag the applied 

 voltage and capacitive reactance causes the cur- 

 rent to lead the applied voltage. These effects 

 tend to neutralize each other, and the combined 

 reactance is the difference between the individual 

 reactances. 



The total opposition offered to the flow of 

 current in an a-c circuit is the impedance , Z. 

 The impedance of a circuit, expressed in ohms, 

 is composed of the capacitive reactance, the 

 inductive reactance, and the resistance. 



The effects of capacitive reactance, inductive 

 reactance, and resistance in an a-c circuit can 

 be shown graphically by the use of vectors. For 

 example, consider the series circuit shown in 

 part A of figure 20-18. 



The vector representation of the reactances 

 is shown in part B of figure 20-18. Because the 

 inductive reactance and the capacitive reactance 

 are exactly opposite, they are subtracted di- 

 rectly and the difference shown in part C of 

 figure 20-18 as capacitive reactance. The re- 

 sultant is found vectorially by constructing a 

 parallelogram, as shown in part D of figure 

 20-18. The resultant vector is also the hypote- 

 nuse of a right triangle; therefore, 



Z= \/r2 + (Xc -Xl)2 



-rVWV\rH(^ 



\\ 



I R 



X -X ' 



Figure 20-18.— Vector solution of an a-c 

 circuit. 



In accordance with Ohm's law for a-c cir- 

 cuits, the effective current through a circuit is 

 directly proportional to the effective voltage and 

 inversely proportional to the impedance. Thus, 



I = -^ 



where 



I = 

 E = 

 Z = 



current, in amperes 



emf, in volts 



impedance, in ohms 



A-C GENERATORS 



Most of the electric power for use aboard 

 ship and ashore is generated by alternating- 

 current generators. 



A-c generators are made in many different 

 sizes, depending upon their intended use. For 

 example, any one of the generators at Boulder 

 Dam can produce millions of volt-amperes, while 

 generators used on aircraft produce only a 

 few thousand volt-amperes. 



Regardless of size, however, all generators 

 operate on the same basic principle: a magnetic 

 field cutting through conductors, or conductors 

 passing through a magnetic field. Thus all 

 generators will have at least two distinct sets 

 of conductors. They are (1) a group of conductors 



505 



