Find the equivalent model of an infinite ladder circuit

In summary, the conversation discusses using Ohm's law and Kirchoff's voltage law to solve a problem involving an infinite circuit. The solution involves finding the total equivalent resistance, applying the loop rule, and using the Thevenin equivalent method to find the emf and internal resistance. The question asks if there is a shorter way to solve the problem.
  • #1
The Blind Watchmaker
17
0

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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  • #2
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
  • #3
Can you show what you mean by replacing the "2nd branch" with a resistor? Perhaps post a picture.
 
  • #4
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.
 

1. What is an infinite ladder circuit?

An infinite ladder circuit is a type of electrical circuit that is composed of an infinite number of identical elements, such as resistors, inductors, or capacitors, arranged in a repeated pattern. This type of circuit is used to model various systems, such as transmission lines, and is often used in theoretical analysis and simulations.

2. How do you find the equivalent model of an infinite ladder circuit?

To find the equivalent model of an infinite ladder circuit, you can use a technique called the "ladder network reduction method." This involves simplifying the circuit by combining repeated patterns of elements into equivalent single elements. This process can be repeated until the circuit is reduced to a more manageable form.

3. What are the benefits of using an equivalent model for an infinite ladder circuit?

Using an equivalent model for an infinite ladder circuit can make it easier to analyze and understand the circuit's behavior. It can also be useful for predicting the circuit's performance under different conditions or making modifications to the circuit design.

4. What are some common applications of infinite ladder circuits?

Infinite ladder circuits can be used in a variety of applications, such as modeling transmission lines, analyzing power distribution systems, and simulating electronic filters. They are also commonly used in theoretical research and circuit design.

5. Are there any limitations to using an equivalent model for an infinite ladder circuit?

While equivalent models can be useful for simplifying and understanding complex circuits, they may not always accurately represent the behavior of a real-world circuit. This is because they rely on certain assumptions and simplifications that may not hold true in all situations. It is important to carefully consider the limitations of an equivalent model when using it in practical applications.

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