Chapter 20. -SHIPBOARD ELECTRICAL SYSTEMS 



Es Es 



Rt Rl R2 R3 



or 



Rt 



= E, 



(^Rl^R2 ^Rs) 



Both sides of this equation may be divided by 

 Eg without changing the value of the equation; 

 therefore, 



Rt Rl R2 R3 



By means of the preceding equation the total 

 resistance of the circuit shown in figure 20-7 

 may be determined. Thus 



Rl IN SERIES WITH PARALLEL COMBINATION OF R2 AND R3 



27.237 

 Figure 20-8.— Compound electric circuit. 



The total resistance, Rt, of figure 20-8 is 

 determined in two steps. First, the resistance 

 R2 3 of the parallel combination of R2 andR3 is 

 determined as 



R 



1 ^X+ -L+ 



10 30 



and 



_1= 10 

 Rt 30 



Taking the reciprocals of both sides, 



30 



R = Yq- = 3 ohms 



A useful rule to remember in computing the 

 equivalent resistance of a d-c parallel circuit 

 is that the total resistance is always less than 

 the smallest resistance in any of the branches. 



In addition to adding the individual branch 

 currents to obtain the total current in a parallel 

 circuit, the total current may be found directly 

 by dividing the applied voltage by the equivalent 

 resistance, R,, For example, in figure 20-7: 



Es ^0 

 I^=— -=-p= 10 amperes 



Rt 



Three or more resistors may be connected 

 in series and parallel combinations to form a 

 compound circuit. One basic series-parallel cir- 

 cuit composed of three resistors is shown in 

 figure 20-8, 



R 



2,3 



^2^3 3x6 18 o . ^ 

 = a — = 2 ohms 



R2 R3 3+6 



The sum of R, „ and R- (that is, Rj is 



Rt = ^2, 3 + Rl = 2 + 2 = 4 ohms 



If the total resistance, Rt, and the source 

 voltage. Eg, are known, the total current. It, 

 may be determined by Ohm's law. Thus, in 

 figure 20-8, 



and 



E . = I,R. = 5 X 2 = 10 volts 

 ab t 1 



E. = LRo , z 5 X 2 = 10 volts 

 be t 2,0 



According to Kirchhoff's voltage law, the 

 sum of the voltage drops around the closed cir- 

 cuit is equal to the source voltage. Thus, 



or 



Eab + Eijc - Eg 



10 + 10 = 20 volts 



If the voltage drop Ebc across R2 3— that is, 

 the drop between points b and c— is known, the 

 current through the individual branches may be 

 determined as 



^bc 10 



3.333 amperes 



Rr 



499 



