Find the resistance between points A and B in a complex circuit

[1/2"]

Homework Statement

Find the resistance between the A and B( image attached)

Homework Equations

The Attempt at a Solution

I could only simplify the diagram to this (2 attached pic) and i can't proceed any further since i can't identy find any parallel or series circuit/

 

[Simon Bridge]

You can unfold the first picture ... put points A and B in the corners, then unfold the triangle point A is on so A is outside the big triangle. See how to simplify it now?
No? Imagine a voltage source V_AB between A and B and you have to find the total current drawn ... now do you get it?

You end up with the resistors forming an H ...

 

[CWatters]

If you redraw it slightly differently you will see that by symetry one R has no voltage across it. So it can be removed without effecting the circuit. Makes it much easier to simplify further.

 

[1/2"]

You can unfold the first picture ... put points A and B in the corners, then unfold the triangle point A is on so A is outside the big triangle. See how to simplify it now?
No? Imagine a voltage source V_AB between A and B and you have to find the total current drawn ... now do you get it?

You end up with the resistors forming an H ...

resistance in between the parallel line of H... how do i combine it with others??
(Thanks A LOT for answering!)

 

[Saitama]

resistance in between the parallel line of H... how do i combine it with others??
(Thanks A LOT for answering!)

If you see carefully, there's a wheat stone bridge.

 

[Simon Bridge]

Pranav-Arora is correct - it's a Wheatstone bridge. How does one of those work?

You may understand it better if you add a DC voltage source to the diagram between A and B ... one of the resistors in the H does not carry a current: so you can just replace it with an open circuit.

If you still don't see it - use Kirkhoffs rules to find the relationship between V_AB and the total current drawn, then Ohm's Law gets you the rest of the way.

 

[azizlwl]

sorry-deleting my post

 

[Simon Bridge]

@aziziwi: I'd have let 1/2" explore the situation in terms of existing knowledge more before introducing new ideas.

Since all the resistors have the same value, there is no need for the Y-Δ transform. Not that it isn't cool to know...

1/2" is about to discover that the problem only looks complicated. Worst case now is that he does a 3-loop/4-node Kirkhoff analysis ... which is lots of work, but sometimes you have to do something the long way before you realize where the shortcut is. Builds character ;)

I think we've gone as close as we can to actually doing the problem ... let's wait for 1/2" to get back to us.