In the network shown in figure each resistance is 1 Ω. The effective resistance between A and B is (a) 4/3 Ω (b) 3/2 Ω (c) 7 Ω (d) 8/7 Ω

Answer: (d). Let VA = 1, VB = 0. By symmetry the bottom middle node is at 12; top-left node at x, top-right at 1-x. KCL at top-left node: (x-1) + (x-12) + (x-(1-x)) = 0 ⇒ x = 58 Current leaving A: (1-12) + (1-58) = 78 A RAB = 1/7/8 = 8/7 Ω. So the answer is (d).

In the network shown in figure each resistance is 1 Ω. The effective… | NEET 1990 (AIPMT)

Q87NEET 1990 · AIPMTMedium

Combination of Resistors

In the network shown in figure each resistance is $1\ \Omega$ . The effective resistance between $A$ and $B$ is

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Answer: (d)

Let $V_A = 1$ , $V_B = 0$ . By symmetry the bottom middle node is at $\tfrac12$ ; top-left node at $x$ , top-right at $1-x$ .
KCL at top-left node: $(x-1) + (x-\tfrac12) + (x-(1-x)) = 0 \Rightarrow x = \tfrac58$
Current leaving A: $(1-\tfrac12) + (1-\tfrac58) = \tfrac78$ A
$R_{AB} = \dfrac{1}{7/8} = \dfrac{8}{7}\ \Omega$ . So the answer is (d).

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