What will be the equivalent resistance between the terminals A and B of the infinite resistive network shown in the figure?

• A

  $\frac{(\sqrt{3}+1) \mathrm{R}}{2}$
• B

  $\frac{(\sqrt{3}-1) R}{2}$
• C

  $3 \frac{R}{2}$
• Correct answer
  D

  $(\sqrt{3}+1) \mathrm{R}$

Solution

Hint:
$x=2 R+\frac{R x}{R+x}$ $x^{2}-2 R x-2 R^{2}=0$ $x=(1+\sqrt{3}) R$

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