What is the Total Resistance of an Infinite Network of Resistors?

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SUMMARY

The total resistance (Rt) of an infinite network of resistors can be determined using a recursive approach that leads to a quadratic equation. In the given configuration, resistors R1 and R2 are arranged in an infinite grid, and the hint indicates that the resistance at any point in the network can be expressed in terms of Rt itself. This self-referential property is key to solving the problem, as it allows for the establishment of a relationship that simplifies the calculation of total resistance.

PREREQUISITES
  • Understanding of electrical resistance and Ohm's Law
  • Familiarity with series and parallel resistor combinations
  • Basic knowledge of quadratic equations and their solutions
  • Concept of infinite series and limits in mathematics
NEXT STEPS
  • Study the derivation of total resistance in infinite resistor networks
  • Learn about recursive equations in electrical circuits
  • Explore the application of quadratic equations in circuit analysis
  • Investigate the concept of equivalent resistance in series and parallel configurations
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Students studying electrical engineering, physics enthusiasts, and anyone tackling complex circuit analysis problems involving infinite resistor networks.

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Homework Statement



Find the total resistance(Rt) of the infinite network.


Allright, what we have is an infinite network of resistors which i will try to make a diagram of here :

b--R1--c---R1-----R1-----R1--- so on
...!...!...!
...!...!...!
...R2...R2...R2 so on (dots are just space fillers to keep it formatted)
...!...!...!
...!...!...!
a---R1--d---R1-----R1-----R1-- so on

A hint says that because it is infinite the resistance at a point to the right of c and d also has R(t)



Homework Equations





The Attempt at a Solution



We tried a whole lot of stuff and ended up with a quadratic equation which gave us some ridiculous answer. Also tried brute force and got nowhere. Please help :)
 
Physics news on Phys.org
The hint is good. And you should get a quadratic equation. Why is your answer crazy? What did you get?
 

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