Find Req. across the terminals A and B. [Figure description: An infinite ladder network of 1 Ω resistors. Terminal A connects through a series 1 Ω resistor on the top rail, terminal B through a series 1 Ω resistor on the bottom rail; after each pair of series resistors a 1 Ω resistor is connected vertically (shunt) between the top and bottom rails, and the pattern (series 1 Ω top, series 1 Ω bottom, shunt 1 Ω) repeats indefinitely to infinity. Req is measured looking into A-B.]
- A. (1 + √2) Ω
- B. (1 + 2√2) Ω
- C. (1 + √3) Ω
- D. (1 + 2√3) Ω
Answer: C. (1 + √3) Ω
Explanation: For the infinite ladder: Req = 1 + 1 + (1 ∥ Req) = 2 + Req/(Req + 1), giving Req² − 2Req − 2 = 0 => Req = 1 + √3 Ω.