DC Circuit Equivalent Resistance Problem

[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 R_AB and R_AC in the question. I do not know the answer for R_AC, but the answer for R_AB 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 R_AB 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 R_AB and R_AC.

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!

 

[gneill]

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.