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NEET 2022 (Phase 2) · Combination of Resistors

Combination of Resistors question from NEET 2022 (Phase 2)

Q42NEET 2022 · PHASE 2Medium

Combination of Resistors

The equivalent resistance of the infinite network given below is:

Figure

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Answer: (d)

  1. Each section has 1 Ω1\ \Omega in each rail and a 1 Ω1\ \Omega rung. Removing one section leaves the same network, so R=1+1+1⋅R1+RR = 1 + 1 + \dfrac{1 \cdot R}{1 + R}.
  2. R(1+R)=2(1+R)+R⇒R2−2R−2=0R(1+R) = 2(1+R) + R \Rightarrow R^2 - 2R - 2 = 0
  3. R=2+4+82=1+3R = \dfrac{2 + \sqrt{4+8}}{2} = 1 + \sqrt{3}
  4. So the answer is (d) (1+3) Ω(1+\sqrt{3})\ \Omega.
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