Infinite Resistor LadderHardQuestion 31663
Question
In an infinite resistor ladder (R in each rung, R between rungs), the input resistance satisfies X² = RX + R², giving:
- AX = R(1+√5)/2Correct
- BX = R(√5−1)/2
- CX = R
- DX = R/2
Correct answer
X = R(1+√5)/2
Explanation
Self-similarity: X = R + XR/(X+R). Solving: X²−RX−R²=0, X = R(1+√5)/2 (golden ratio × R). Only positive root accepted.