# DC Circuit Equivalent Resistance Problem

• shantam777
In summary, The conversation is about a student asking for help with a circuit problem involving the calculation of equivalent resistance. They apologize for not fully complying with the rules and ask for advice on simplifying the circuit. The person responding offers a hint about using symmetry as a tool to simplify the circuit.
shantam777
Hello guys,
My teacher gave me a question regarding calculation of equivalent resistance, trying to solve which I'm losing my sanity. I feel a bit ashamed because this is my first post and I'm using it to ask a doubt, a little selfish of me. But it's kind of urgent so I don't really have a choice. Now I've read the rules and I know I'm going a little out of the line, because in order to show the circuit I'm going to have to attach an image, and also that I have made numerous attempts at the solution and all of them are wrong, so I don't know if I should attach them or not. Should I attach anyone of them? The values of all the resistors in the circuit is R, and we have to find RAB and RAC in the question. I do not know the answer for RAC, but the answer for RAB is (3/2)R, or 1.5R. If anyone can show me how can I simplify the circuit in order to get the value of RAB as 1.5R, I will be EXTREMELY grateful! I just need to know the correct way of how to simplify this circuit, because I've tried many different approaches, all resulting in different and incorrect answers. Thanks for reading, and I sincerely apologize for not fully complying to the rules here, I would be grateful if anyone could point out how I can follow them and still ask my question properly. Thanks I've attached the image of the circuit (Sorry for my horrible drawing skills) .

## Homework Statement

Simplify the given circuit and obtain the values of RAB and RAC.

## Homework Equations

None, I've attached the image of the circuit. The values of all the resistors in the circuit is R.

## The Attempt at a Solution

All my attempts are wrong. Should I just attach anyone of them? Help me out here please!

#### Attachments

• PhyQ.jpg
53.7 KB · Views: 460
Last edited:
Hi shantam777, Welcome to Physics Forums.

It's fine to attach images that pertain to the problem being asked. You should post or attach at least one of your attempts and describe where it seemed to go wrong or where you got stuck. Attempt at solution is a mandatory inclusion.

I will offer you a hint: A very powerful tool can be the use of symmetry. Any nodes in the circuit that you know will have the same potential (assuming that you imagine a voltage source applied across the terminals of interest, such as a-b) can be connected by a wire without changing how the circuit works. Why? Because if they are at the same potential then no current will flow through that wire anyways. You can then consider them to be the same single node. This will allow you to collapse the circuit since symmetrical pairs of components will be rendered parallel and can be reduced to single components.

## What is a DC circuit?

A DC circuit is a closed loop of electrically conductive material that allows current to flow in one direction, powered by a Direct Current (DC) source such as a battery or power supply.

## What is equivalent resistance in a DC circuit?

Equivalent resistance is the single resistance that could replace all the resistors in a DC circuit and produce the same overall resistance. It is calculated by adding all the individual resistances in series, or using the formula for parallel resistors.

## How do you calculate equivalent resistance in a series circuit?

In a series circuit, equivalent resistance is calculated by adding all the individual resistances together. For example, if there are three resistors in series with values of 10 ohms, 20 ohms, and 30 ohms, the equivalent resistance would be 10 + 20 + 30 = 60 ohms.

## How do you calculate equivalent resistance in a parallel circuit?

In a parallel circuit, equivalent resistance is calculated using the formula 1/Req = 1/R1 + 1/R2 + ... + 1/Rn where Req is the equivalent resistance and R1, R2, etc. are the individual resistances. For example, if there are two resistors in parallel with values of 10 ohms and 20 ohms, the equivalent resistance would be 1/Req = 1/10 + 1/20 = 3/20, therefore Req = 20/3 = 6.67 ohms.

## Why is equivalent resistance important in DC circuits?

Equivalent resistance is important in DC circuits because it allows us to simplify complex circuits into a single resistance, making it easier to calculate current and voltage. It also helps us understand the overall behavior of the circuit and make predictions about its performance.

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