Principles of naval engineering - Historic Naval Ships Association

Chapter 20. -SHIPBOARD ELECTRICAL SYSTEMSorEsEsRt Rl R2 R3Rt= E, (^Rl^R2 ^Rs)Both sides of this equation may be divided byEg without changing the value of the equation;therefore,Rt Rl R2 R3By means of the preceding equation the totalresistance of the circuit shown in figure 20-7may be determined. ThusRl IN SERIES WITH PARALLEL COMBINATION OF R2 AND R3Figure 20-8.— Compound electric circuit.27.237The total resistance, Rt, of figure 20-8 isdetermined in two steps. First, the resistanceR2 3 of the parallel combination of R2 andR3 isdetermined asandR 1^X+ -L+10 30_1= 10Rt 30R 2,3^2^3 3x6 18 o. ^= a — = 2 ohmsR2 R3 3+6The sum of R, „ and R- (that is, Rj isRt = ^2, 3 + Rl = 2 + 2 = 4 ohmsTaking the reciprocals of both sides,30R = Yq-=3 ohmsA useful rule to remember in computing theequivalent resistance of a d-c parallel circuitis that the total resistance is always less thanthe smallest resistance in any of the branches.In addition to adding the individual branchcurrents to obtain the total current in a parallelcircuit, the total current may be found directlyby dividing the applied voltage by the equivalentresistance, R,, For example, in figure 20-7:Es^0I^=—-=-p= 10 amperesRtThree or more resistors may be connectedin series and parallel combinations to form acompound circuit. One basic series-parallel circuitcomposed of three resistors is shown infigure 20-8,If the total resistance, Rt, and the sourcevoltage. Eg, are known, the total current. It,may be determined by Ohm's law. Thus, infigure 20-8,andE . = I,R. = 5 X 2 = 10 voltsab t 1E. = LRo , z 5 X 2 = 10 voltsbe t 2,0According to Kirchhoff's voltage law, thesum of the voltage drops around the closed circuitis equal to the source voltage. Thus,orEab + Eijc - Eg10 + 10 = 20 voltsIf the voltage drop Ebc across R2 3— that is,the drop between points b and c— is known, thecurrent through the individual branches may bedetermined as^bc 10Rr3.333 amperes499