Infinite R-chain: Find Resistance Between A and B

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SUMMARY

The discussion focuses on calculating the equivalent resistance of an infinite chain of resistors, each with a resistance of 90 Ω. The problem requires determining the resistance of a single resistor that can be connected between points A and B, which would match the resistance of the infinite chain. The user attempts to simplify the problem by first considering the equivalent resistance of three 90 Ω resistors in series, indicating a methodical approach to finding a pattern in the resistance values.

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  • Understanding of series and parallel resistor configurations
  • Knowledge of Ohm's Law and equivalent resistance calculations
  • Familiarity with infinite series concepts in electrical circuits
  • Basic algebra for solving equations related to resistances
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Homework Statement


Consider the infinite chain of resistors shown above and suppose that each resistor in the chain has a resistance of 90 Ω. What is the resistance of a single resistor that could be connected between A and B with the same resistance as that of the infinite chain?


Homework Equations


A------R-------R--------R--->
- - -
R R R to infinity
- - -
B------R-------R--------R--->
This is the best I could do to show the chain of resistors. It is the equivalent of a series of boxes with a resistor on each side.

The Attempt at a Solution


 
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Lets start off with a somewhat easier example:

What is the equivalent resistance of three 90 ohm resistors in series? 4? 5? Notice a pattern?
 

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