Find total resistance between A and B

In summary, the homework statement says that the student is trying to find the total resistance between two points, A and B. The student tries to use Kirchhoff's Laws to solve for the resistance, but finds that the resistance is not the same between A and B. The student then tries to find the resistance by imagining the wire as parallel and calculating the resistance. The student finds that the resistance is 20/13 R.
  • #1

Homework Statement [Broken]
Find total resistance between A and B

The Attempt at a Solution

Well, first I tried using Kirchhoff's Laws to find the resistance, but that ended up being a total mess so here's what I tried, not sure if it is correct.

Can the (R+R) and 2R branch on the left, be combined to 1R? I was thinking that this would be correct because the same amount current should be on each side of A.
If that is correct, then I can simply do R + 2R (right side resistance in parallel) = 3R. (I think)

Is this correct, or do I need to use Kirchoff's laws to solve?
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  • #2
Very good. Yes, in this case you are able to use parallel & series combination simplifications to get the total resistance. There can be more complex situations, however where you would need to use the KCL equations and solve for the intermediate voltages and currents in order to figure out the total resistance.

But in this case, the simpler way is the best way.
  • #3
I do not believe this method is quite correct. Hmmm... difficult to illustrate it without a diagram...

You see, the problem is that current flows through the wire in the middle. If you connect a potential difference across A and B, the current on both sides of A(or B) will not be the same hence the resistance will not be the same measured from A to B.

A right way I think would be is to have a sort of parallel combination of 4 possible paths current can get through from A to B. i.e. Have 4 wires with resistance:
and imagine them as parallel.
And then calculate it. You should get something like 20/13 R.

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