How Do You Calculate the Equivalent Resistance in an Infinite Resistor Network?

In summary, the conversation discusses the method for calculating the equivalent resistance of a resistor chain with an infinite length and equal resistance values. The solution involves replacing the chains with their equivalent resistances and considering sub-chains to the left and right of a point. This method can be applied to both parts a) and b) of the homework problem.
  • #1
Saitama
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Homework Statement


Calculate the equivalent resistance of the resistor chain shown in the figure between the points a) A and B; b) A and C the resistor chain is infinite in both directions and each resistor has a resistance of R.
41137ec21c802ca3495bb5597.gif

Homework Equations


The Attempt at a Solution


I have solved the b) part. It is the part a) which I face trouble with. How do I approach this?

Any help is appreciated. Thanks!
 
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  • #2
You have the equivalent resistance of both the chain to the left from A and the one to the right from B. Replace the chains with their equivalent resistances in the figure.

ehild
 
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  • #3
I would add point D just below B and consider the sub-chains to the left of AC and to the right of BD (with the resistor between A and C or B and C). These sub-chains should have equal resistances. Then the entire ABDC loop can be represented as four resistors.
 
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  • #4
By the way, if you solved part (b) in some other way, you can obtain the equivalent resistance of each sub-chain from that result, and then solve part (a).
 
  • #5
ehild said:
You have the equivalent resistance of both the chain to the left from A and the one to the right from B. Replace the chains with their equivalent resistances in the figure.

ehild

voko said:
I would add point D just below B and consider the sub-chains to the left of AC and to the right of BD (with the resistor between A and C or B and C). These sub-chains should have equal resistances. Then the entire ABDC loop can be represented as four resistors.

Thanks ehild and voko! That did the trick. :)

I solved the part b) with the same method but couldn't observe that you could do the same with a). :redface:
 

Related to How Do You Calculate the Equivalent Resistance in an Infinite Resistor Network?

What is an infinite resistors circuit?

An infinite resistors circuit is a theoretical circuit that consists of an infinite number of resistors connected in series or parallel. It is used to understand the behavior of circuits with a large number of resistors.

What is the purpose of studying infinite resistors circuits?

The study of infinite resistors circuits helps scientists to understand the fundamental principles of circuits, such as Ohm's law and Kirchhoff's laws. It also allows for the prediction of the behavior and characteristics of real-world circuits with a large number of resistors.

What are the key components of an infinite resistors circuit?

The key components of an infinite resistors circuit are resistors, power source, and connecting wires. The resistors can be either connected in series or parallel, and the power source provides the electrical energy required for the circuit to function.

How does an infinite resistors circuit differ from a real-world circuit?

An infinite resistors circuit is a theoretical circuit that has an infinite number of resistors, whereas a real-world circuit has a finite number of resistors. Additionally, real-world circuits may have other components like capacitors and inductors, which are not present in an infinite resistors circuit.

What are the limitations of using infinite resistors circuits in practical applications?

Infinite resistors circuits are useful for understanding the behavior of circuits with a large number of resistors, but they have limitations when applied to real-world circuits. This is because real-world circuits have a finite number of components and other factors like temperature, noise, and parasitic effects that can affect their behavior, which cannot be accounted for in an infinite resistors circuit.

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