CUET Preparation Today
The equivalent resistance between points A and B of an infinite network of resistances, each of 1Ω, connected as shown, is:
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infinite 2Ω $\frac{1+\sqrt{5}}{2}$ Ω zero |
$\frac{1+\sqrt{5}}{2}$ Ω |
Let RAB = x. Then,
$R_{AB}=1+\frac{x}{1+x}$ or $x=1+\frac{x}{1+x}$ ∴ $x+x^2=1+x+x$ or $x^2-x-1=0$ $x=\frac{1+\sqrt{1+4}}{2}=\frac{1+\sqrt{5}}{2} \Omega$ |
