Question

The equivalent resistance of the following infinite network of resistances is

• A. Less than $4\Omega$
• B. $4\Omega$
• C. More than $4\Omega$ but less than $12\Omega$
• D. $12\Omega$

Answer 1

Answer: (C)

More than $4\Omega$ but less than $12\Omega$

Answer 2

Similar

$R = 2 + 2 + \frac{2 \times R}{2 + R}$ ⇒ $2R + R^{2} = 8 + 4R + 2R$

⇒ $R^{2} - 4R - 8 = 0$ ⇒ $R = \frac{4 \pm \sqrt{16 + 32}}{2} = 2 \pm 2\sqrt{3}$

R cannot be negative, hence

$R = 2 + 2\sqrt{3} = 5.46\Omega$