The equivalent resistance of the infinite network given below is:

The equivalent resistance of the infinite network given below is:

1. $2 \Omega$
2. $(1+\sqrt{2}) \Omega$
3. $(1+\sqrt{3}) \Omega$
4. $(1+\sqrt{5}) \Omega$

Solution

Let net resistance of the given infinite network be ' \(R\) '
Now, the circuit can be modified as

Now, \(R_{\text {net }}=R=1+1+\frac{R}{R+1}\)
$\begin{aligned} & \therefore R=2+\frac{R}{R+1} \\ & R^{2}+R=2R+2+R \\ & R^{2}-2R-2=0 \\ & R=\frac{2 \pm \sqrt{4+8}}{2} \\ & R=(1+\sqrt{3}) \, \Omega \end{aligned}$

Asked in: NEET 2022 (Phase 2)

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