Principles of naval engineering - Historic Naval Ships Association

Chapter 20. -SHIPBOARD ELECTRICAL SYSTEMSwhere•71fLinductive reactance, in ohms3.1416frequency, in cycles per secondinductance, in henrys-rVWV\rH(^\\The current flowing in a capacitive circuitis directly proportional to the capacitance and tothe rate at which the applied voltage is changing.The rate at which the voltage changes is determinedby the frequency. The value of the capacitivereactance, Xq, is inversely proportional tothe capacitance of the circuit and the frequencyof the applied voltage. Thus,IRwhere127rfCX -X 'TTfc= capacitive reactance, in ohms= 3.1416= frequency, in cycles per second= capacitance, in faradsThe effects of capacitance and inductance inan a-c circuit are exactly opposite. Inductivereactance causes the current to lag the appliedvoltage and capacitive reactance causes the currentto lead the applied voltage. These effectstend to neutralize each other, and the combinedreactance is the difference between the individualreactances.The total opposition offered to the flow ofcurrent in an a-c circuit is the impedance , Z.The impedance of a circuit, expressed in ohms,is composed of the capacitive reactance, theinductive reactance, and the resistance.The effects of capacitive reactance, inductivereactance, and resistance in an a-c circuit canbe shown graphically by the use of vectors. Forexample, consider the series circuit shown inpart A of figure 20-18.The vector representation of the reactancesis shown in part B of figure 20-18. Because theinductive reactance and the capacitive reactanceare exactly opposite, they are subtracted directlyand the difference shown in part C offigure 20-18 as capacitive reactance. The resultantis found vectorially by constructing aparallelogram, as shown in part D of figure20-18. The resultant vector is also the hypotenuseof a right triangle; therefore,Z= \/r2 + (Xc -Xl)2Figure20-18.— Vector solution of an a-ccircuit.In accordance with Ohm's law for a-c circuits,the effective current through a circuit isdirectly proportional to the effective voltage andinversely proportional to the impedance. Thus,whereI = -^I = current, in amperesE = emf, in voltsZ = impedance, in ohmsA-C GENERATORSMost of the electric power for use aboardship and ashore is generated by alternatingcurrentgenerators.A-c generators are made in many differentsizes, depending upon their intended use. Forexample, any one of the generators at BoulderDam can produce millions of volt-amperes, whilegenerators used on aircraft produce only afew thousand volt-amperes.Regardless of size, however, all generatorsoperate on the same basic principle: a magneticfield cutting through conductors, or conductorspassing through a magnetic field. Thus allgenerators will have at least two distinct setsof conductors. They are (1) a group of conductors505