Question

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

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

Answer 1

Answer: (C)

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

Answer 2

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 $R _ { e q } = R _ { o } + \left( R \| R _ { e q } \right)$

$= R + \frac{RR_{eq}}{R + R_{eq}} \Rightarrow R_{eq} = \frac{1}{2}\lbrack 1 + \sqrt{5}\rbrack$