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

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

c (c) By formula $R = {R_1} + \frac{{{R_2} \times R}}{{{R_2} + R}}$ $R = 1 + \frac{{1 \times R}}{{1 + R}}$ $==>$ ${R^2} + R = 1 + R + R$ $==>$ ${R^2} - R - 1 = 0$ 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 $

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

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

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

Diffcult

STD 11 Science
NEET
STD 12 - 3. current electricity
Physics

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