Question

The equivalent resistance between points $A$ and $B$ of an infinite network of resistances, each of $1\Omega$, connected as shown in fig. is

• A. Infinite
• B. $2\Omega$
• C. $\frac{1+\sqrt{5}}{2}\Omega$
• D. Zero

Answer 1

Answer: (C)

$\frac{1+\sqrt{5}}{2}\Omega$

Similar Q. No 30. By formula $R=R_1+\frac{R_2\times R}{R_2+R}$

$\therefore R=1+\frac{1\times R}{1+R}\Rightarrow R^2+R=1+R+R$

$\Rightarrow R^2-R-1=0$ or $R=\frac{1\pm \sqrt{1+4}}{2}=\frac{1\pm \sqrt{5}}{2}$

Since $R$ cannot be negative, hence $R=\frac{1+\sqrt{5}}{2}\Omega$