Question

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

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

Answer 1

The correct option is C $\frac{1+\sqrt{5}}{2}\Omega$

Suppose the effective resistance between A and B is $R_{eq}$. Since the network consists of infinite cell. If we exclude one cell from the chain, remaining network have infinite cells i.e. effective resistance between C and D will also $R_{eq}$.

So now $R_{eq}=R_0+(R\parallel R_{eq})=R+\frac{R{R}_{eq}}{R+R_{eq}}\Rightarrow R_{eq}=\frac{1}{2}[1+\sqrt{5}]$