The equivalent resistance of the infinite network given below is:

• A

  $2 \Omega$
• B

  $(1+\sqrt{2}) \Omega$
• Correct answer
  C

  $(1+\sqrt{3}) \Omega$
• D

  $(1+\sqrt{5}) \Omega$

Solution

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

Hence, the correct answer is option: 'C'.