32 



HANDBOOK OF MECHANICAL DESIGN 



TOTAL RESISTANCE OF PARALLEL CIRCUITS 



1 



J_+± + ±+± + ... 

 Ri R2 Rz Ri 



For convenience, list the resistances of the different parallel circuits in descending order 

 of magnitude. Locate Ri on the diagonal scale and connect it with ^2 on the hori- 

 zontal scale. The total resistance is found at the intersection with the Total Resistance 

 diagonal. For more than two parallel circuits, project horizontally from the intersec- 

 tion point on the Total Resistance diagonal to the diagonal Resistance Ri, draw a 

 line to i? 3 on the horizontal scale, and the answer will again be found at the 

 intersection with the Total Resistance diagonal. Repeat successively for 

 additional resistances Rt, Ri, etc. 



The light dashed lines indicate the procedure for finding the total 

 resistance of five parallel circuits, Ri =100, R^ = 60, Rs = 40, 

 Ri = 30, Rti = 25. The answer as given by the chart is 8.0. 



Conversely, the resistances of individual parallel cir- 

 cuits to give a desired total resistance can be determined 

 from this chart. 



f i r |ll l l | llll | ll l l |ll l Ol l M|llll|l ll l[ lll l|ll ll|I UI| lll lpl l l| l ll l | l lll|ll l l|nil |l l ll |N I I|l lll|MII|lll 



10 20 30 40 50 60 70 80 90 100 110 120 



50 60 70 80 



Resisi'ances, R2,R3,R4"" 



