A electric circuit (in the picture) is given where all the resistance are of 1 ohm. I have to find its equivalent resistance. (9,10, 11th points are conncections)
My attempt: I think electron flow will follow 2 paths: 1 2 9 3 10 4 11 5 6 and 1 8 7 6. So the resistances of these 2 paths are in series combination. So, equiavalent resistance of path 1 and 2 respictively are 2 and 3 ohm. As these 2 paths are in parallel the equivalent resistance would be 6/5 ohm.
Am I right? I am assuming that 3 short-circuits are present (2 9 3, 3 10 4, 4 11 5) in those 3 subcycles of the whole circuit.
I think my attempt is wrong. Any hint?
Answer
Current will take all possible paths. There are more than 2 possible paths, and they are not connected in series or parallel.
First try simplifying the circuit. The resistors on the top row are all shorted out, so they can be removed without affecting the circuit. The diagonal resistors are connected at the top and bottom to the vertical resistors, so these are in parallel; there are 2 resistors in parallel at the LH and RH branches, and 3 in the middle two branches.
You can then apply Kirchhoff's Rules to the simplified circuit, making use of symmetry. Alternatively, a combination of 3 resistors connected to the same node can be replaced by 3 resistors arranged in a triangle, using the $Y-\Delta$ Transformation. All of the resistors are then in series or parallel.
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