# Can I find a general solution to this circuit?

• Lotto
In summary, the conversation discusses finding an equivalent resistance for a circuit with multiple ##R_3## resistors. The speaker mentions using a general solution and suggests looking up "ladder circuit" methods. They also mention a relationship between the resistance of the circuit and the number of ##R_3## resistors, making it easier to solve for large values of ##n##.
Lotto
Thread moved from the technical forums to the schoolwork forums
TL;DR Summary: I have to find an equivalent resistance of the circuit below, dependent on the amount of ##R_3## - resistors.

Here is the circuit:

I think there is no general solution. When I want to calculate it, I have to do ##((((R_1+2R_2)^{-1}+{R_3}^{-1})^{-1}+2R_2)^{-1}+{R_3}^{-1})^{-1}...##, so it is kind of crazy. Is there any general solution dependent on the amount of ##R_3## - resistors ##n##? So something like ##R_{\mathrm {eq} _n}=....##.

Google "ladder circuit". You will find methods for dealing with problems like this.

Lotto said:
TL;DR Summary: I have to find an equivalent resistance of the circuit below, dependent on the amount of ##R_3## - resistors.

Here is the circuit:
View attachment 326155
I think there is no general solution. When I want to calculate it, I have to do ##((((R_1+2R_2)^{-1}+{R_3}^{-1})^{-1}+2R_2)^{-1}+{R_3}^{-1})^{-1}...##, so it is kind of crazy. Is there any general solution dependent on the amount of ##R_3## - resistors ##n##? So something like ##R_{\mathrm {eq} _n}=....##.
My first step would be to leave out the two R1s. Those can be put back in later.
The resistance of the remaining system is a function R(n). Can you figure out the relationship between R(n) and R(n+1)?

haruspex said:
My first step would be to leave out the two R1s. Those can be put back in later.
The resistance of the remaining system is a function R(n). Can you figure out the relationship between R(n) and R(n+1)?
Yes, I did it and I made an approximation when ##n## is big, so we can say that ##R_n \approx R_{n-1}##, similary as when we solve an infinite ladder circuit. Then it was easy to solve.

## 1. What is a general solution to a circuit?

A general solution to a circuit is a mathematical equation or set of equations that describes the behavior of the circuit for all possible inputs and conditions. It allows for the prediction of the circuit's response to any input or change in its components.

## 2. Why is finding a general solution important?

Finding a general solution is important because it provides a comprehensive understanding of how the circuit works and allows for the optimization of its design. It also enables engineers to troubleshoot and make modifications to the circuit more effectively.

## 3. Is it possible to find a general solution to any circuit?

In theory, it is possible to find a general solution to any circuit. However, in practice, the complexity and non-linearity of some circuits make it difficult to find an exact solution. In these cases, approximations or numerical methods may be used.

## 4. What factors affect the difficulty of finding a general solution to a circuit?

The difficulty of finding a general solution to a circuit depends on its complexity, the number of components, and the type of components used. Non-linear components, such as transistors, can also make it more challenging to find a general solution.

## 5. Can computer simulations be used to find a general solution to a circuit?

Yes, computer simulations can be used to find a general solution to a circuit. By inputting the circuit's parameters and conditions, simulations can accurately predict the circuit's behavior and provide a general solution. However, it is still important to verify the results with real-world testing.

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