Figure shows an infinite ladder network of resistances. The equivalent resistance between points X and Y is

Question

Figure shows an infinite ladder network of resistances. The equivalent resistance between points X and Y is, infinite, 3 Ω, 8.62 Ω, 1.62 Ω

MARKS App · Accepted Answer

Let R e q be the equivalent resistance of this network. ⇒ R eq = 1 + R eq × 1 1 + R eq ⇒ R + R 2 = 1 + R + R ⇒ R 2 - R - 1 = 0 ⇒ R = 1 ± 1 + 4 × 1 2 × 1 ⇒ R = 1 ± 5 2 ⇒ R =1.62 Ω

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