Question

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

• A. $\frac{(\sqrt{3}+1)}{2}$
• B. $\frac{(\sqrt{3}-R)}{2}$
• C. $3\frac{R}{2}$
• D. $(\sqrt{3}+1)R$

Answer 1

The correct option is D $(\sqrt{3}+1)R$

Let $R^{\prime }$ be the equivalent resistance
The circuit can be redrawn as
$\Rightarrow R_{equ}=\frac{R{R}^{\prime }}{R+R^{\prime }}+2R{R}^{\prime }=\frac{R{R}^{\prime }}{R+R^{\prime }}+2R$
Solving & neglecting negative value
$R^{\prime }=R(\sqrt{3}+1)$