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.
closed as off-topic by Emilio Pisanty, ZeroTheHero, John Rennie, Jon Custer, M. Enns Jan 8 at 16:40
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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.
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.
(2) Look for symmetries in the circuit. In this case the right hand end is an upside down version of the left hand end, and that enables you to label everything in terms of three unknown currents. Find their values using Kirchhoff II.