Let's take this circuit as an example !

How to find the resistance between A and B ? and between B and C ???
Why can't i just say that the resistance between A and B is the equivalent of the three resistances in parallel since they're the only ones between these two points ?

 

But their not the only three resistances between A and B. Current can also flow to the left and up to point C and then down the leftmost resistor. Similarly, it can go out to the right and up and then over and down the rightmost resistor.

The most general way to find the resistance between two points is to take a test voltage source and apply it between those two points. Then see how much current flows in the source as a result. Divide the voltage by the current and you have the effective resistance.

In this case, you can exploit symmetry to find the resistance between A and B pretty easily. Doing so between B and C is a bit trickier. Sometimes redrawing the circuit so that the layout is more what you expect to work with can help.

 

Let's take this circuit as an example !
View attachment 141850
How to find the resistance between A and B ? and between B and C ???
Why can't i just say that the resistance between A and B is the equivalent of the three resistances in parallel since they're the only ones between these two points ?

Hi,

One trick that is used is to place a current source across the two nodes you need to know the resistance between, then solve for the voltage across those two nodes, then R=V/I.

In this circuit however there is another trick because there is perfect left to right symmetry. That means there is a trick you can use that mostly depends on that top most resistor "r" drawn horizontally. It may not be apparent at first, but if you look long enough and think a little, you will see that both resistances can be quickly found by realizing the trick you can do with that top most resistor.

Symmetry is something that helps solve many problems in physics so when you find it there's always some trick you can use. Just takes a littel thought, well sometimes a lot of thought as in string theory.

I dont want to give too much away just yet, but i will give a hint. Think about what the node voltages on each side of the network might be, how they are related to each other.