Question

The given figure shows an infinite ladder network of resistances. The equivalent resistance between points A and B is. 

(A) Infinite 

(B) 3.73Ω 

(C) 2.73Ω 

(D) (2/3)Ω

Answer 1

The correct option (C) 2.73Ω

Explanation:

Let resistance of infinite ladder be R. The circuit can be drawn as hence

R = (R || 1) + 1 + 1

= 2 + {(R × 1) / (R + 1)}

R = 2 + {R/(R + 1)}

∴ R – {R/(R + 1)} = 2

R² + R – R – 2R – 2 = 0

R² – 2R – 2 = 0

∴ R = 2.73Ω