As shown in the diagram, network of resistors R1 and R2 extends off to infinity to the right. Find the equivalent resistance.


Let equivalent resistance between A and B be RNote: To the right of C and D we have a circuit similar to that in figure one, i.e. at C and D we have R connected in parallel to R2See figure 2Reistance between CD, RCD=R2RR2+RNow R=RAC+RCD+RBDR=R1+R2RR2+R+R1R-R2RR2+R=2R1R2+R2R-R2RR2+R=2R1R2R2+R=2R1R2=2R1R+2R1R2R2-2R1R-2R1R2=0R=--2R1±-2R12-4-2R1R22R=--2R1±4R12+2R1R22R=2R1±2R12+2R1R22R=R1±R12+2R1R2Sinc Resistance is positiveR=R1+R12+2R1R2
 

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