Question

Figure shows an infinite ladder network of resistances. The equivalent resistance between points $X$ and $Y$ is-

• A. infinite
• B. $3\Omega$
• C. $8.62\Omega$
• D. $1.62\Omega$

Answer 1

The correct option is D $1.62\Omega$

$\begin{array}{c}R=1+\frac{R}{1+R}\\ \Rightarrow R\left(1+R\right)=1+2R\\ \Rightarrow R^2-R-1=0\\ R=\frac{1+\sqrt{1+4}}{2}\\ =\frac{1+\sqrt{5}}{2}=1.62\Omega \end{array}$

$\therefore$ Option $D$ is correct.