GATE 2016 EC (EC2) – Question 40
Every resistor in the circuit is $1\ \Omega$. The equivalent resistance between a and b is
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Correct answer: (D) $8/15\ \Omega$
Explanation
Apply 1 V between a and b. By reflection symmetry, the outer right vertex and the innermost right vertex are both at 1/2 V, so their connecting resistor carries no current.
Let the upper inner node be u; the lower is 1−u. Its node equation is $(u-1)+(u-(1-u))+(u-1/2)=0$, giving u=5/8.
Current from a is $1+(1-1/2)+(1-5/8)=15/8$ A. Thus $R_{ab}=1/(15/8)=$ **8/15 Ω, D**.