# What is the equivalent resistance between $A$ and $B$ in the given circuit? [closed]

Hi, I've been doing some current electricity problems by using Kirchhoff's laws. I've tried applying KVL(Kirchhoff Voltage law) to this circuit, but to no avail. There happens to be too many variables to work on with my approach. I would appreciate if I could get some help regarding solving this problem and similar ones.

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• This is a symmetry question, often the central resistor carries no current due to symmetry, i.e. both side are at the same potential. – PhysicsDave Jan 6 at 20:43
• But here the central R does have current. The way to solve is to see 2 paths. Path 1 is A to D to F to B, note that D to F equates to 0.5R so this paths 2.5R. Path 2 is A to C to E to B, in this path we get 3R (note central R has zero I). Combine the 2 paths in parallel. – PhysicsDave Jan 6 at 20:52

The way to solve is to see 2 paths. Path 1 is $$A$$ to $$D$$ to $$F$$ to $$B$$, note that $$D$$ to $$F$$ equates to $$0.5R$$ so this path is $$2.5R$$. Path 2 is $$A$$ to $$C$$ to $$E$$ to $$B$$, in this path we get $$3R$$ (note central $$R$$ has zero $$I$$). Combine the 2 paths in parallel.
• Well, it gives the right answer, but how does it work? Why does D to F equate to 0.5 $R?$ Why do you say that the "central $R$ has zero $I"?$ None of the resistors has zero current. Would you please spell out your method more fully? – Philip Wood Jan 6 at 23:13
Here are two hints. (1) Apply Kirchhoff I at the junctions on the diagram itself, by labelling the currents $$x,$$ $$y,$$ $$(x-y)$$ (or whatever is right), and so on. In other words, don't waste time writing formal Kirchhoff I equations, and don't call the currents $$"I_1",$$ $$"I_2"$$ etc.