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GATE 2014 EC (EC4) – Question 42

Networks, Signals and Systems · Circuit Analysis · 2 marks · Numerical answer

Find R_e/R for the infinite ladder shown.

Diagram for GATE 2014 EC (EC4) question 42

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Correct answer: 2.60 to 2.64

Explanation

Let the repeating shunt-tail resistance be xR. Self-similarity gives x=1∥(1+x)=(1+x)/(2+x), so x²+x−1=0. The physical positive root is(√5−1)/2. The initial series resistor is2R, hence Re/R=2+x=(3+√5)/2=**2.618034**.