Find the equivalent model of an infinite ladder circuit

AI Thread Summary
The discussion focuses on finding the equivalent model of an infinite ladder circuit using Ohm's law and Kirchhoff's voltage law. The original poster calculated the total equivalent resistance as 2r and determined the effective emf to be 2ε. They inquired about potentially shorter methods for solving the problem. A suggestion was made to use the Thevenin equivalent to simplify the analysis. Clarification was requested regarding the replacement of the second branch with a resistor, indicating a need for visual representation.
The Blind Watchmaker
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Homework Statement


upload_2018-3-6_22-1-0.png


2. Homework Equations
Ohm's law and Kirchoff's voltage law

The Attempt at a Solution


My solution is a bit long so I will just briefly explain it. First, we find the total equivalent resistance. Since the circuit extends to infinity, it is equal to replacing the second branch onward by a single resistor. After some calculus, Req = 2r. Thus, internal resistance is 2r. Next, apply the loop rule to find the current before it terminates as it is physically impossible for the current to blow up to infinity. Effective emf is found to be 2Ir = 2ε.

My question is, is there perhaps another (shorter) way to solve this problem? If so, please explain your solution. Thanks!
 

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The Blind Watchmaker said:

Homework Statement


View attachment 221489

2. Homework Equations
Ohm's law and Kirchoff's voltage law

The Attempt at a Solution


My solution is a bit long so I will just briefly explain it. First, we find the total equivalent resistance. Since the circuit extends to infinity, it is equal to replacing the second branch onward by a single resistor. After some calculus, Req = 2r. Thus, internal resistance is 2r. Next, apply the loop rule to find the current before it terminates as it is physically impossible for the current to blow up to infinity. Effective emf is found to be 2Ir = 2ε.

My question is, is there perhaps another (shorter) way to solve this problem? If so, please explain your solution. Thanks!
Your method and your results are correct. You can use Thevenin equivalent. Adding the unit in the red frame to the equivalent source of emf E and internal resistance Ri, the emf and internal resistance of the Thevenin equivalent between A and B are E and Ri, respectively.

upload_2018-3-6_17-8-18.png
 

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Likes scottdave
Can you show what you mean by replacing the "2nd branch" with a resistor? Perhaps post a picture.
 
ehild said:
You can use Thevenin equivalent. Adding the unit in the red frame to the equivalent source of emf E and internal resistance Ri,...

View attachment 221497
Now I'll buy that. I appeared as if the OP was going to replace everything beyond the first source with just a resistor.
 

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