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NEET 2022
Exam
NEET
Year
2022
Subject
Physics
Chapter
Current Electricity

NEET 2022 · Physics · Current Electricity

The equivalent resistance of the infinite network given below is:

The equivalent resistance of the infinite network given below is: The equivalent resistance of the infinite network given below is:

Options

  1. A2Ω2 \Omega
  2. B(1+2)Ω(1+\sqrt{2}) \Omega
  3. C(1+3)Ω(1+\sqrt{3}) \Omega
  4. D(1+5)Ω(1+\sqrt{5}) \Omega

Correct answer

C. (1+3)Ω(1+\sqrt{3}) \Omega

Step-by-step solution

Let net resistance of the given infinite network be ' RR ' Now, the circuit can be modified as Now, (R_{\text{net }}=R=1+1+\frac{R}{R+1}) ∴R=2+RR+1R2+R=2R+2+RR2−2R−2=0R=(2±4+82)R=(1+3)Ω\begin{aligned} & \therefore R=2+\frac{R}{R+1} \\ & R^2+R=2 R+2+R \\ & R^2-2 R-2=0 \\ & R=\left(\frac{2 \pm \sqrt{4+8}}{2}\right) \\ & R=(1+\sqrt{3}) \Omega \end{aligned})$
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